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Worksheets for simplifying expressions

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Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

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Mixed problem types, solving multi-step equations.

Solve a mix of equation types involving like terms

This worksheet is a combination of problem types from this category. All problems may be flipped and contain negative coefficients, but they always resolve to integers.

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Solving Systems Linear Equations (pdf) of Mixed problems on solving systems of linear equations

Students will practice solving systems of equations .

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Directions: Solve each system of linear equations

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Algebra Worksheets

Welcome to the Algebra worksheets page at Math-Drills.com, where unknowns are common and variables are the norm. On this page, you will find Algebra worksheets for middle school students on topics such as algebraic expressions, equations and graphing functions.

This page starts off with some missing numbers worksheets for younger students. We then get right into algebra by helping students recognize and understand the basic language related to algebra. The rest of the page covers some of the main topics you'll encounter in algebra units. Remember that by teaching students algebra, you are helping to create the future financial whizzes, engineers, and scientists that will solve all of our world's problems.

Algebra is much more interesting when things are more real. Solving linear equations is much more fun with a two pan balance, some mystery bags and a bunch of jelly beans. Algebra tiles are used by many teachers to help students understand a variety of algebra topics. And there is nothing like a set of co-ordinate axes to solve systems of linear equations.

Most Popular Algebra Worksheets this Week

Combining Like Terms and Solving Simple Linear Equations

Algebraic Properties, Rules and Laws Worksheets

solving linear equations mixed practice worksheet

The commutative law or commutative property states that you can change the order of the numbers in an arithmetic problem and still get the same results. In the context of arithmetic, it only works with addition or multiplication operations , but not mixed addition and multiplication. For example, 3 + 5 = 5 + 3 and 9 × 5 = 5 × 9. A fun activity that you can use in the classroom is to brainstorm non-numerical things from everyday life that are commutative and non-commutative. Putting on socks, for example, is commutative because you can put on the right sock then the left sock or you can put on the left sock then the right sock and you will end up with the same result. Putting on underwear and pants, however, is non-commutative.

  • The Commutative Law Worksheets The Commutative Law of Addition (Numbers Only) The Commutative Law of Addition (Some Variables) The Commutative Law of Multiplication (Numbers Only) The Commutative Law of Multiplication (Some Variables)

The associative law or associative property allows you to change the grouping of the operations in an arithmetic problem with two or more steps without changing the result. The order of the numbers stays the same in the associative law. As with the commutative law, it applies to addition-only or multiplication-only problems. It is best thought of in the context of order of operations as it requires that parentheses must be dealt with first. An example of the associative law is: (9 + 5) + 6 = 9 + (5 + 6). In this case, it doesn't matter if you add 9 + 5 first or 5 + 6 first, you will end up with the same result. Students might think of some examples from their experience such as putting items on a tray at lunch. They could put the milk and vegetables on their tray first then the sandwich or they could start with the vegetables and sandwich then put on the milk. If their tray looks the same both times, they will have modeled the associative law. Reading a book could be argued as either associative or nonassociative as one could potentially read the final chapters first and still understand the book as well as someone who read the book the normal way.

  • The Associative Law Worksheets The Associative Law of Addition (Whole Numbers Only) The Associative Law of Multiplication (Whole Numbers Only)

Inverse relationships worksheets cover a pre-algebra skill meant to help students understand the relationship between multiplication and division and the relationship between addition and subtraction.

  • Inverse Mathematical Relationships with One Blank Addition and Subtraction Easy Addition and Subtraction Harder All Multiplication and Division Facts 1 to 18 in color (no blanks) Multiplication and Division Range 1 to 9 Multiplication and Division Range 5 to 12 Multiplication and Division All Inverse Relationships Range 2 to 9 Multiplication and Division All Inverse Relationships Range 5 to 12 Multiplication and Division All Inverse Relationships Range 10 to 25
  • Inverse Mathematical Relationships with Two Blanks Addition and Subtraction (Sums 1-18) Addition and Subtraction Inverse Relationships with 1 Addition and Subtraction Inverse Relationships with 2 Addition and Subtraction Inverse Relationships with 3 Addition and Subtraction Inverse Relationships with 4 Addition and Subtraction Inverse Relationships with 5 Addition and Subtraction Inverse Relationships with 6 Addition and Subtraction Inverse Relationships with 7 Addition and Subtraction Inverse Relationships with 8 Addition and Subtraction Inverse Relationships with 9 Addition and Subtraction Inverse Relationships with 10 Addition and Subtraction Inverse Relationships with 11 Addition and Subtraction Inverse Relationships with 12 Addition and Subtraction Inverse Relationships with 13 Addition and Subtraction Inverse Relationships with 14 Addition and Subtraction Inverse Relationships with 15 Addition and Subtraction Inverse Relationships with 16 Addition and Subtraction Inverse Relationships with 17 Addition and Subtraction Inverse Relationships with 18

The distributive property is an important skill to have in algebra. In simple terms, it means that you can split one of the factors in multiplication into addends, multiply each addend separately, add the results, and you will end up with the same answer. It is also useful in mental math, an example of which should help illustrate the definition. Consider the question, 35 × 12. Splitting the 12 into 10 + 2 gives us an opportunity to complete the question mentally using the distributive property. First multiply 35 × 10 to get 350. Second, multiply 35 × 2 to get 70. Lastly, add 350 + 70 to get 420. In algebra, the distributive property becomes useful in cases where one cannot easily add the other factor before multiplying. For example, in the expression, 3(x + 5), x + 5 cannot be added without knowing the value of x. Instead, the distributive property can be used to multiply 3 × x and 3 × 5 to get 3x + 15.

  • Distributive Property Worksheets Distributive Property (Answers do not include exponents) Distributive Property (Some answers include exponents) Distributive Property (All answers include exponents)

Students should be able to substitute known values in for an unknown(s) in an expression and evaluate the expression's value.

  • Evaluating Expressions with Known Values Evaluating Expressions with One Variable, One Step and No Exponents Evaluating Expressions with One Variable and One Step Evaluating Expressions with One Variable and Two Steps Evaluating Expressions with Up to Two Variables and Two Steps Evaluating Expressions with Up to Two Variables and Three Steps Evaluating Expressions with Up to Three Variables and Four Steps Evaluating Expressions with Up to Three Variables and Five Steps

As the title says, these worksheets include only basic exponent rules questions. Each question only has two exponents to deal with; complicated mixed up terms and things that a more advanced student might work out are left alone. For example, 4 2 is (2 2 ) 2 = 2 4 , but these worksheets just leave it as 4 2 , so students can focus on learning how to multiply and divide exponents more or less in isolation.

  • Exponent Rules for Multiplying, Dividing and Powers Mixed Exponent Rules (All Positive) Mixed Exponent Rules (With Negatives) Multiplying Exponents (All Positive) Multiplying Exponents (With Negatives) Multiplying the Same Exponent with Different Bases (All Positive) Multiplying the Same Exponent with Different Bases (With Negatives) Dividing Exponents with a Greater Exponent in Dividend (All Positive) Dividing Exponents with a Greater Exponent in Dividend (With Negatives) Dividing Exponents with a Greater Exponent in Divisor (All Positive) Dividing Exponents with a Greater Exponent in Divisor (With Negatives) Powers of Exponents (All Positive) Powers of Exponents (With Negatives)

Knowing the language of algebra can help to extract meaning from word problems and to situations outside of school. In these worksheets, students are challenged to convert phrases into algebraic expressions.

  • Translating Algebraic Phrases into Expressions Translating Algebraic Phrases into Expressions (Simple Version) Translating Algebraic Phrases into Expressions (Complex Version)

Combining like terms is something that happens a lot in algebra. Students can be introduced to the topic and practice a bit with these worksheets. The bar is raised with the adding and subtracting versions that introduce parentheses into the expressions. For students who have a good grasp of fractions, simplifying simple algebraic fractions worksheets present a bit of a challenge over the other worksheets in this section.

  • Simplifying Expressions by Combining Like Terms Simplifying Linear Expressions with 3 terms Simplifying Linear Expressions with 4 terms Simplifying Linear Expressions with 5 terms Simplifying Linear Expressions with 6 to 10 terms
  • Simplifying Expressions by Combining Like Terms with Some Arithmetic Adding and simplifying linear expressions Adding and simplifying linear expressions with multipliers Adding and simplifying linear expressions with some multipliers . Subtracting and simplifying linear expressions Subtracting and simplifying linear expressions with multipliers Subtracting and simplifying linear expressions with some multipliers Mixed adding and subtracting and simplifying linear expressions Mixed adding and subtracting and simplifying linear expressions with multipliers Mixed adding and subtracting and simplifying linear expressions with some multipliers Simplify simple algebraic fractions (easier) Simplify simple algebraic fractions (harder)
  • Rewriting Linear Equations Rewrite Linear Equations in Standard Form Convert Linear Equations from Standard to Slope-Intercept Form Convert Linear Equations from Slope-Intercept to Standard Form Convert Linear Equations Between Standard and Slope-Intercept Form
  • Rewriting Formulas Rewriting Formulas (addition and subtraction; about one step) Rewriting Formulas (addition and subtraction; about two steps) Rewriting Formulas ( multiplication and division ; about one step)

Linear Expressions and Equations

solving linear equations mixed practice worksheet

In these worksheets, the unknown is limited to the question side of the equation which could be on the left or the right of equal sign.

  • Missing Numbers in Equations with Blanks as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Blanks in Any Position )
  • Missing Numbers in Equations with Symbols as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Symbols in Any Position )
  • Solving Equations with Addition and Symbols as Unknowns Equalities with Addition (0 to 9) Symbol Unknowns Equalities with Addition (1 to 12) Symbol Unknowns Equalities with Addition (1 to 15) Symbol Unknowns Equalities with Addition (1 to 25) Symbol Unknowns Equalities with Addition (1 to 99) Symbol Unknowns
  • Missing Numbers in Equations with Variables as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Variables Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Variables in Any Position )
  • Solving Simple Linear Equations Solving Simple Linear Equations with Values from -9 to 9 (Unknown on Left Side) Solving Simple Linear Equations with Values from -99 to 99 (Unknown on Left Side) Solving Simple Linear Equations with Values from -9 to 9 (Unknown on Right or Left Side) Solving Simple Linear Equations with Values from -99 to 99 (Unknown on Right or Left Side)
  • Determining Linear Equations from Slopes, y-intercepts and Points Determine a Linear Equation from the Slope and y-intercept Determine a Linear Equation from the Slope and a Point Determine a Linear Equation from Two Points Determine a Linear Equation from Two Points by Graphing

Graphing linear equations and reading existing graphs give students a visual representation that is very useful in understanding the concepts of slope and y-intercept.

  • Graphing Linear Equations Graph Slope-Intercept Equations
  • Determinging Linear Equations from Graphs Determine the Equation from a Graph Determine the Slope from a Graph Determine the y-intercept from a Graph Determine the x-intercept from a Graph Determine the slope and y-intercept from a Graph Determine the slope and intercepts from a Graph Determine the slope, intercepts and equation from a Graph

Solving linear equations with jelly beans is a fun activity to try with students first learning algebraic concepts. Ideally, you will want some opaque bags with no mass, but since that isn't quite possible (the no mass part), there is a bit of a condition here that will actually help students understand equations better. Any bags that you use have to be balanced on the other side of the equation with empty ones.

Probably the best way to illustrate this is through an example. Let's use 3 x + 2 = 14. You may recognize the x as the unknown which is actually the number of jelly beans we put in each opaque bag. The 3 in the 3 x means that we need three bags. It's best to fill the bags with the required number of jelly beans out of view of the students, so they actually have to solve the equation.

On one side of the two-pan balance, place the three bags with x jelly beans in each one and two loose jelly beans to represent the + 2 part of the equation. On the other side of the balance, place 14 jelly beans and three empty bags which you will note are required to "balance" the equation properly. Now comes the fun part... if students remove the two loose jelly beans from one side of the equation, things become unbalanced, so they need to remove two jelly beans from the other side of the balance to keep things even. Eating the jelly beans is optional. The goal is to isolate the bags on one side of the balance without any loose jelly beans while still balancing the equation.

The last step is to divide the loose jelly beans on one side of the equation into the same number of groups as there are bags. This will probably give you a good indication of how many jelly beans there are in each bag. If not, eat some and try again. Now, we realize this won't work for every linear equation as it is hard to have negative jelly beans, but it is another teaching strategy that you can use for algebra.

Despite all appearances, equations of the type a/ x are not linear. Instead, they belong to a different kind of equations. They are good for combining them with linear equations, since they introduce the concept of valid and invalid answers for an equation (what will be later called the domain of a function). In this case, the invalid answers for equations in the form a/ x , are those that make the denominator become 0.

  • Solving Linear Equations Combining Like Terms and Solving Simple Linear Equations Solving a x = c Linear Equations Solving a x = c Linear Equations including negatives Solving x /a = c Linear Equations Solving x /a = c Linear Equations including negatives Solving a/ x = c Linear Equations Solving a/ x = c Linear Equations including negatives Solving a x + b = c Linear Equations Solving a x + b = c Linear Equations including negatives Solving a x - b = c Linear Equations Solving a x - b = c Linear Equations including negatives Solving a x ± b = c Linear Equations Solving a x ± b = c Linear Equations including negatives Solving x /a ± b = c Linear Equations Solving x /a ± b = c Linear Equations including negatives Solving a/ x ± b = c Linear Equations Solving a/ x ± b = c Linear Equations including negatives Solving various a/ x ± b = c and x /a ± b = c Linear Equations Solving various a/ x ± b = c and x /a ± b = c Linear Equations including negatives Solving linear equations of all types Solving linear equations of all types including negatives

Linear Systems

solving linear equations mixed practice worksheet

  • Solving Systems of Linear Equations Easy Linear Systems with Two Variables Easy Linear Systems with Two Variables including negative values Linear Systems with Two Variables Linear Systems with Two Variables including negative values Easy Linear Systems with Three Variables; Easy Easy Linear Systems with Three Variables including negative values Linear Systems with Three Variables Linear Systems with Three Variables including negative values
  • Solving Systems of Linear Equations by Graphing Solve Linear Systems by Graphing (Solutions in first quadrant only) Solve Standard Linear Systems by Graphing Solve Slope-Intercept Linear Systems by Graphing Solve Various Linear Systems by Graphing Identify the Dependent Linear System by Graphing Identify the Inconsistent Linear System by Graphing

Quadratic Expressions and Equations

solving linear equations mixed practice worksheet

  • Simplifying (Combining Like Terms) Quadratic Expressions Simplifying quadratic expressions with 5 terms Simplifying quadratic expressions with 6 terms Simplifying quadratic expressions with 7 terms Simplifying quadratic expressions with 8 terms Simplifying quadratic expressions with 9 terms Simplifying quadratic expressions with 10 terms Simplifying quadratic expressions with 5 to 10 terms
  • Adding/Subtracting and Simplifying Quadratic Expressions Adding and simplifying quadratic expressions. Adding and simplifying quadratic expressions with multipliers. Adding and simplifying quadratic expressions with some multipliers. Subtracting and simplifying quadratic expressions. Subtracting and simplifying quadratic expressions with multipliers. Subtracting and simplifying quadratic expressions with some multipliers. Mixed adding and subtracting and simplifying quadratic expressions. Mixed adding and subtracting and simplifying quadratic expressions with multipliers. Mixed adding and subtracting and simplifying quadratic expressions with some multipliers.
  • Multiplying Factors to Get Quadratic Expressions Multiplying Factors of Quadratics with Coefficients of 1 Multiplying Factors of Quadratics with Coefficients of 1 or -1 Multiplying Factors of Quadratics with Coefficients of 1, or 2 Multiplying Factors of Quadratics with Coefficients of 1, -1, 2 or -2 Multiplying Factors of Quadratics with Coefficients up to 9 Multiplying Factors of Quadratics with Coefficients between -9 and 9

The factoring quadratic expressions worksheets in this section provide many practice questions for students to hone their factoring strategies. If you would rather worksheets with quadratic equations, please see the next section. These worksheets come in a variety of levels with the easier ones are at the beginning. The 'a' coefficients referred to below are the coefficients of the x 2 term as in the general quadratic expression: ax 2 + bx + c. There are also worksheets in this section for calculating sum and product and for determining the operands for sum and product pairs.

  • Factoring Quadratic Expressions Factoring Quadratic Expressions with Positive 'a' coefficients of 1 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients of 1 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients of 1 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 4 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 4 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 4 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 5 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 5 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 5 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 9 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 9 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 9 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 81 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 81 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 81 with a Common Factor Step Calculating Sum and Product (Operand Range 0 to 9 ) ✎ Calculating Sum and Product (Operand Range 1 to 9 ) ✎ Calculating Sum and Product (Operand Range 0 to 9 Including Negatives ) ✎ Calculating Sum and Product (Operand Range 1 to 9 Including Negatives ) ✎ Calculating Sum and Product (Operand Range -20 to 20 ) ✎ Calculating Sum and Product (Operand Range -99 to 99 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 9 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 9 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 12 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 12 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 9 Including Negatives ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 9 Including Negatives ) ✎ Determining Operands from Sum and Product Pairs (Operand Range -20 to 20 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range -99 to 99 ) ✎

Whether you use trial and error, completing the square or the general quadratic formula, these worksheets include a plethora of practice questions with answers. In the first section, the worksheets include questions where the quadratic expressions equal 0. This makes the process similar to factoring quadratic expressions, with the additional step of finding the values for x when the expression is equal to 0. In the second section, the expressions are generally equal to something other than x, so there is an additional step at the beginning to make the quadratic expression equal zero.

  • Solving Quadratic Equations that Equal Zero Solving Quadratic Equations with Positive 'a' coefficients of 1 Solving Quadratic Equations with Positive or Negative 'a' coefficients of 1 Solving Quadratic Equations with Positive or Negative 'a' coefficients of 1 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 4 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 4 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 4 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 5 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 5 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 5 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 9 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 9 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 9 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 81 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 81 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 81 with a Common Factor Step
  • Solving Quadratic Equations that Equal an Integer Solving Quadratic Equations for x ("a" coefficients of 1) Solving Quadratic Equations for x ("a" coefficients of 1 or -1) Solving Quadratic Equations for x ("a" coefficients up to 4) Solving Quadratic Equations for x ("a" coefficients between -4 and 4) Solving Quadratic Equations for x ("a" coefficients up to 81) Solving Quadratic Equations for x ("a" coefficients between -81 and 81)

Other Polynomial and Monomial Expressions & Equations

solving linear equations mixed practice worksheet

  • Simplifying Polynomials That Involve Addition And Subtraction Addition and Subtraction; 1 variable; 3 terms Addition and Subtraction; 1 variable; 4 terms Addition and Subtraction; 2 variables; 4 terms Addition and Subtraction; 2 variables; 5 terms Addition and Subtraction; 2 variables; 6 terms
  • Simplifying Polynomials That Involve Multiplication And Division Multiplication and Division; 1 variable; 3 terms Multiplication and Division; 1 variable; 4 terms Multiplication and Division; 2 variables; 4 terms Multiplication and Division; 2 variables; 5 terms
  • Simplifying Polynomials That Involve Addition, Subtraction, Multiplication And Division All Operations; 1 variable; 3 terms All Operations; 1 variable; 4 terms All Operations; 2 variables; 4 terms All Operations; 2 variables; 5 terms All Operations (Challenge)
  • Factoring Expressions That Do Not Include A Squared Variable Factoring Non-Quadratic Expressions with No Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Compound Coefficients, and Negative and Positive Multipliers
  • Factoring Expressions That Always Include A Squared Variable Factoring Non-Quadratic Expressions with All Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Compound Coefficients, and Negative and Positive Multipliers
  • Factoring Expressions That Sometimes Include Squared Variables Factoring Non-Quadratic Expressions with Some Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Compound Coefficients, and Negative and Positive Multipliers
  • Multiplying Polynomials With Two Factors Multiplying a monomial by a binomial Multiplying two binomials Multiplying a monomial by a trinomial Multiplying a binomial by a trinomial Multiplying two trinomials Multiplying two random mon/polynomials
  • Multiplying Polynomials With Three Factors Multiplying a monomial by two binomials Multiplying three binomials Multiplying two binomials by a trinomial Multiplying a binomial by two trinomials Multiplying three trinomials Multiplying three random mon/polynomials

Inequalities

solving linear equations mixed practice worksheet

  • Writing The Inequality That Matches The Graph Writing Inequalities for Graphs
  • Graphing Inequalities On Number Lines Graphing Inequalities (Basic)
  • Solving Linear Inequalities Solving Inequalities Including a Third Term Solving Inequalities Including a Third Term and Multiplication Solving Inequalities Including a Third Term, Multiplication and Division

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Differentiated WORKSHEET on Solving Equations (with Answers)

Differentiated WORKSHEET on Solving Equations (with Answers)

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Outstanding Resources

Last updated

23 November 2022

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solving linear equations mixed practice worksheet

This has always been an effective worksheet, clearly showing the different leveled steps of solving equations.

This is one of the worksheets that accompanies the three lesson bundle on solving equations that is available from Outstanding Resources. The lessons are very structured and easy to follow. What really sets them apart is the superb teaching slides and the amount of custom animation as well as additional resources. The first lesson in the bundle is linked below:

Solving Equations - Lesson 1

LASTLY: This lesson is flat packed for copyright purposes. Please provide a RATING with written feedback. Please email  [email protected]  if there are any issues and we will respond within 48 hours.

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Empty reply does not make any sense for the end user

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Nice idea, but you should never write 1x it must be x.

Same, same and for a lot of students it is helpful for understanding. Equally not something examination boards penalise either. Glad you enjoyed the resource.

Thank you - some lovely questions, nicely structured

Thanks for the rating and review. Andrew from Outstanding Resources

Thanks for the rating. Andrew from Outstanding Resources

Differentiated questions on a page and answers on a page, PERFECT! Thank you for sharing

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Linear equations require students to work with a single variable of degree 1. So solving them are pretty simple and can be attempted by kids in grades 6-8.

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Algebra - Mixed Practice (Up to Quadratic Equations)

solving linear equations mixed practice worksheet

These worksheets are an immediate follow-up to the worksheet set on factoring; the new content in these worksheets is solving quadratic equations in one variable by factoring.

Included are problems in which no rearranging of terms is needed, followed by problems in which rearranging of terms is required. The third worksheet includes a variety of word problems solvable through factoring.

In each worksheet, some linear equations are included as part of the material review, since students have a tendency to fixate on one type of problem or the other; being able to recognize which type of problem they're looking at, and then to recognize the process used to solve it, is very important.

The final worksheet is focused entirely on solving word problems. It contains a mix of linear and quadratic word problems.

Worksheet 6.1

  • Distributive property and combining like terms
  • Solving linear equations
  • Solving quadratic equations (no rearranging)

Worksheet 6.2

  • Writing expressions
  • Solving quadratic equations (with rearranging)

Worksheet 6.3

  • Mixed linear and quadratic equations
  • Solving word problems with quadratic equations

Worksheet 6.4

  • Mixed linear and quadratic word problems

Worksheet Sets in this Series

Worksheets for this section are below the index. Click the "Overview" link to get a more detailed view of the entire series.

  • Mixed Practice Overview
  • Mixed Practice #1 - Pre-Algebra
  • Mixed Practice #2 - Algebraic Expressions
  • Mixed Practice #3 - Linear Equations
  • Mixed Practice #4 - Polynomial Manipulation
  • Mixed Practice #5 - Factoring
  • Mixed Practice #6 - Quadratic Equations
  • Mixed Practice #7 - Rational Expressions
  • Mixed Practice #8 - Systems of Equations
  • Mixed Practice #9 - Radical Expressions

Handouts/Worksheets

Mixed practice 6.1.

  • 3x 2 + 2x + 5x - x 2 =   
  • 2(3x + 1) + 2x(x + 1) =  
  • 1 2 x - 1 3 x 2 - 1 5 x + 2 5 x 2  
  • 2x[3x - 5(1 - x) + 1] =  
  • 5 - {4 - [3 - (2 - 1)]} =  Solve the linear equations  
  • 2x + 7 = 35  
  • 11x - 10 = 12  
  • 2(x + 4) = 18  
  • 3(2x - 1) + 5 = 54  
  • 2(x + 1) = 3(x - 1) - 5 Solve the quadratic equations  
  • (x - 3)(x + 5) = 0  
  • (2x - 1)(5x - 2) = 0  
  • (x + 7)(2x + 1) = 0  
  • x 2 - 8x + 7 = 0  
  • x 2 - 3x - 28 = 0  
  • 3x 2 + 4x - 7 = 0  
  • 2x 2 + 8x + 8 = 0  
  • x 2 - 16 = 0  
  • 18x 2 - 2 = 0  
  • 6x 2 - 7x + 1 = 0

Mixed Practice 6.1: Answer Key

Mixed practice 6.2.

  • The sum of a number and four less than that number =  
  • Four less than the product of five and a number =  
  • The difference between twice a number and half the number =   
  • Five times the difference between a number and seven =   
  • A price increased by half of a percent =   
  • A price increased by three hundred percent =   
  • The product of a number and two less than that number =  Solve the linear equations  
  • 2 3 (x + 6) = 12  
  • 0.2(0.1x - 0.5) = 0.42x  
  • 3x + 2 5 x = 17 Solve the quadratic equations  
  • 2x 2 + 9x = 11  
  • 4 9 x 2 - 80 = 1  
  • x 2 = 4x - 4  
  • 2x(x + 1) = 84  
  • (x - 1)(x + 5) = 72  
  • 5(x + 1) = 3x(x - 2) + 15  
  • (x + 1) 2 + (x + 2) 2 = (x + 3) 2  
  • 3(x - 1) 2 + 4(x - 1) = 1 - x  
  • 1 3 x 2 + x = - 2 3  
  • x 2 + 8x + 8 = 2x - 1

Mixed Practice 6.2: Answer Key

Mixed practice 6.3.

Solve the equations below. 

  • x 2 - 7x = -12  
  • 4(x + 2) = 2x + 42  
  • -3(x - 1) = 9  
  • (x + 1)(x - 3) = 21  
  • 2 3 (x + 1) = 12  
  • 5x + 2(3x - 1 2 ) = 65  
  • 3x(x - 1) = (x + 1)(x - 2) + 42  
  • 5x 2 = 3x 2 + 2(5x + 14)  
  • 10(2x + 1 2 ) = 25  
  • x(x - 9) = 36 Solve the word problems  
  • The product of a number and 12 more than that number is -27. What is the largest of the possible numbers?  
  • The length of a rectangle is two less than its width. The area is 80. What are the rectangle's dimensions?  
  • If twice a number is decreased by 7, and the result is multiplied by the number, the final result is 30. What are the possible values of the number?  
  • The square of a number is equal to four times the number plus 12 more. What are the possible values of the number?  
  • The height of an object off the ground after has been launched is given by the equation h = 64.4t- 16.1t 2 , where t is time since the launch. How many seconds long will the object's flight be? [Hint: The object's flight is over at the moment it hits the ground. You will get two t values; one of them is zero, which represents the moment the object was launched, not the time it landed]  
  • In the previous problem, after how many seconds will its height off the ground be 48.3 feet? [Hint: all the numbers in the equation are multiples of 16.1; factor this number out before factoring the quadratic]

Mixed Practice 6.3: Answer Key

Mixed practice 6.4.

  • A number, plus twice that number, plus fifteen, is forty-five more than the number. What is the number?  
  • Two less than a number is multiplied by two more than the number, and the result is four less than seven times the number. What is the number?  
  • The price of a dozen eggs $1.80 less than the price of eighteen eggs. Assuming the same price per egg, how much does a single egg cost?  
  • The profit Ellen makes (in cents) selling lemonade is 1 12 n 2 - 1 3 n, where n is the number of cups she sells. How many cups does she need to sell to make a profit of $0.33? [Hint: multiply both sides of the equation by 12, and then solve]  
  • David's average score for three tests was 76. His first two scores where 70.4 and 74. What is the third score?  
  • A positive number, plus twice the square of that number, is 45. What is the number?  
  • Two more than a number, multiplied by three less than a number is nineteen less than the square off the number. What is the number?  
  • The area of a rectangle is 88 square units. The length is five less than twice the width. What is the length of the rectangle?  
  • The perimeter of a rectangle is 88 units. The length is five less than twice the width. What is the width of the rectangle?  
  • Jack is five years older than Mack. Next year, the product of their ages will be 104. What is Jack's age now?  
  • If a number is doubled, and the result is tripled, and then 5 is subtracted, the result is 85. What is the number?  
  • Two is added to a negative number, and the result is squared. Then the number is added. The final result is 108. What is the original number?  
  • A number is doubled, and the result is multiplied by two more than the number. The result is 286. What is the number?  
  • The cost, in cents, of an item is 12 more than the number of items purchased. $1.08 was spent. How much did one item cost?  
  • Five times a number squared, minus that number is the product of three times the number with seven more than the number. If the number is positive, what is the number?

Mixed Practice 6.4: Answer Key

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Solving One-Step Equation Worksheets

One-step equation worksheets have exclusive pages to solve the equations involving fractions, integers, and decimals. Perform the basic arithmetic operations - addition, subtraction, multiplication and division to solve the equations. Exercises on the application of the equations in real life are available here to impart practical knowledge. This set of printable worksheets is specially designed for 6th grade, 7th grade, and 8th grade students. Free sample worksheets are included.

Integers: Mixed Operations | Level 1

Integers: Mixed Operations | Level 1

A variety of one-step equations involving all the four basic operations are given in these mixed operation pdf worksheets. Perform the appropriate operation and solve for the unknown variable.

  • Download the set

Integers: Mixed Operations | Level 2

Integers: Mixed Operations | Level 2

Taking your practice a step higher, the coefficients are rendered in positive and negative integers. Retain the variable on one side, take the coefficient and constant to the other side and solve.

Fractions: Mixed Operations | Level 1

Fractions: Mixed Operations | Level 1

Add, subtract, multiply, and divide to solve the one-step fraction equations in these level 1 worksheets that involve proper and improper fractions as coefficients and constants.

Fractions: Mixed Operations | Level 2

Fractions: Mixed Operations | Level 2

A moderate practice awaits 7th grade and 8th grade students here! Solve a series of one-step equations with their terms incorporating fractions as well as mixed numbers.

Decimals: Mixed Operations

Decimals: Mixed Operations

The terms of the one-step equations in these worksheets are either decimals or integers. All four arithmetic operations are involved here to solve the problems.

Integers, Fractions and Decimals

Integers, Fractions and Decimals

In these printable worksheets, the coefficient of each one-step equation may be an integer, fraction or decimal. Complete practice can be given to children by solving these equations.

One Step Equation Word Problems Worksheets

One Step Equation Word Problems Worksheets

Employ this assembly of one-step equation word problems featuring integers, decimals and fraction coefficients.

(15 Worksheets)

Solve and Verify the Solution - Integers

Solve and Verify the Solution

Solve each one-step equation to find the unknown variable. Substitute the value of the variable in the given equation to verify the solution of the equation. This set of worksheets is ideal for students of grade 7 and grade 8.

One-Step Equation MCQs | Integers

One-Step Equation MCQs | Integers

Plenty of multiple choice questions are available in these handouts. Solve the indicated equations and choose the correct integer values from the given options.

One-Step Equation MCQs | Fractions

One-Step Equation MCQs | Fractions

Solving equations, finding the equation with a given solution, and evaluating expressions with the obtained values are the skills you can acquire in these pdf MCQ worksheets featuring fractions.

Cost of the Product

Cost of the Product

These printable worksheets contain an activity based exercise to find the cost of the products. The price tags of the objects are represented in an equation form. Solve the equations.

Translating One-Step Equation

Translating One-Step Equation

Children in grade 6 should read each verbal phrases / sentences and translate it to an appropriate one-step linear equation.

What Number am I?

What Number am I?

Guess my number! These fun math riddles help kids to easily understand and translate the sentences into equations. Try all these interesting problems.

Application in Geometry: Type 1

Application in Geometry: Type 1

Enhance your knowledge by solving these one-step equations on geometry. In 'Type 1' pdf worksheets, find the unknown sides of the given shape by solving the one-step equations.

Application in Geometry: Type 2

Application in Geometry: Type 2

'Type 2' printable worksheets contain problems based on applications in geometry. Apply the properties of shapes to find the unknown parameter(s).

Related Worksheets

» Two-Step Equation

» Multi-Step Equation

» Equation Word Problems

» Simplifying Algebraic Expressions

» Translating Phrases

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  2. Linear Equations

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  3. PDF Solving Multi-Step Equations

    {−1} {−1} 14) {−3} {1} 15) {0} {0} 18) {−2} No solution. {−3} {−7} (1) Divide by 5 first, or (2) Distribute the 5 first. Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com

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    Worksheets for linear equations Find here an unlimited supply of printable worksheets for solving linear equations, available as both PDF and html files. You can customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more.

  5. Combining Like Terms and Solving Simple Linear Equations (A)

    Students can use math worksheets to master a math skill through practice, in a study group or for peer tutoring. Use the buttons below to print, open, or download the PDF version of the Combining Like Terms and Solving Simple Linear Equations (A) math worksheet. The size of the PDF file is 40996 bytes. Preview images of the first and second (if ...

  6. PDF Mixed Review of Solving Equations

    Mixed Review of Solving Equations Aim: To review solving equations in different forms Standard(s): 7.A.4 Do Now: Worksheet is titled " How much do you know about Solving Equations" Instructional material: Students will watch a short video clip from the website: www.brainpop.com ~ "Solving two-step equations".

  7. Mixed Problem Types Solving Multi-Step Equations

    Create a worksheet: Solve a mix of equation types involving like terms

  8. Algebra

    Introduced in this set are problems involving setting up and solving basic one-variable equations. Worksheet 3.1. In this worksheet we ask students to write expressions and equations, but do not ask them to solve. multiplying and dividing fractions; percentages; writing algebraic expressions; writing equations; Worksheet 3.2

  9. Solving Systems Linear Equations (pdf) of Mixed problems on solving

    Free worksheet (pdf) and answer key on solving systems of equations --using substitution, elimination and a graph. 21 scaffolded questions that start relatively easy and end with some real challenges. Plus model problems explained step by step

  10. PDF Solving Systems of Equations Mixed Practice Worksheet 1

    Solving Systems of Equations Mixed Practice Worksheet 1 Solve each system of equations. 1. 4 + 5 = 23 9 − 5 = −62 2. + 4 = 25 3 − 6 = −33 3. 8 = 72 ... Solving Systems of Equations Mixed Practice Worksheet 1 Answers Solve each system of equations. 1. 4 + 5 = 23 9 − 5 = −62 (−3,7) 2. + 4 = 25

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    Recommendations. Skill plans. IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Solve linear equations: mixed review" and thousands of other math skills.

  12. PDF I. Model Problems. II. Practice III. Challenge Problems VI. Answer Key

    You can solve systems of linear equations by graphing, the elimination method, or by substitution. To solve by graphing, graph both of the linear equations in the system. The solution to the system is the point of intersection of the two lines. It's best to use the graphing approach when you are given two lines in slope-intercept form.

  13. Solving Equations Textbook Exercise

    The Corbettmaths Textbook Exercise on Solving Equations. ... Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths ... Solving Equations Textbook Exercise. Click here for Questions. Textbook Exercise. Previous: Equations involving Fractions Textbook Exercise. Next: Negative Scale Factors Textbook ...

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    Click here for Answers. equation, solve. Practice Questions. Previous: Ray Method Practice Questions. Next: Equations involving Fractions Practice Questions. The Corbettmaths Practice Questions on Solving Equations.

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    Here is a set of practice problems to accompany the Linear Equations section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University.

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  17. Differentiated WORKSHEET on Solving Equations (with Answers)

    This is one of the worksheets that accompanies the three lesson bundle on solving equations that is available from Outstanding Resources. The lessons are very structured and easy to follow. What really sets them apart is the superb teaching slides and the amount of custom animation as well as additional resources.

  18. Solving Linear Equations Worksheets

    Lesson and Practice. Write equation that matches the balance picture. Then find X. Here 'X' and a negative number are on one side of the balance; and a positive number is on the other side of the balance. There are 3 negative numbers and 6 positive numbers. Rearrange the terms so that all the numbers are on one side and X is on the other side.

  19. Linear Equations Worksheets with Answer Key

    Linear equations require students to work with a single variable of degree 1. So solving them are pretty simple and can be attempted by kids in grades 6-8. More Linear Equations Worksheets Graphing Linear Equations Worksheets Linear Equations Word Problems Worksheets Systems of Linear Equations worksheets Writing Equations of Lines Worksheets

  20. Solving Equation Worksheets

    One-step equation worksheets. This set of worksheets requires students to solve one-step equations involving integers, fractions and decimals by performing addition, subtraction, multiplication or division operations. It also contains math riddles, finding the cost of the objects, translating the phrases into one-step equation and more.

  21. Systems of Equations

    Graphing Systems: Where's the Meeting? Free math worksheets for systems of equations, including solving systems by graphing, substitution, or elimination - also includes word problems.

  22. Algebra

    Mixed Practice #1 - Pre-Algebra Mixed Practice #2 - Algebraic Expressions Mixed Practice #3 - Linear Equations Mixed Practice #4 - Polynomial Manipulation Mixed Practice #5 - Factoring Mixed Practice #6 - Quadratic Equations Mixed Practice #7 - Rational Expressions Mixed Practice #8 - Systems of Equations Mixed Practice #9 - Radical Expressions

  23. Solving One-Step Equation Worksheets

    A variety of one-step equations involving all the four basic operations are given in these mixed operation pdf worksheets. Perform the appropriate operation and solve for the unknown variable. Download the set Integers: Mixed Operations | Level 2 Taking your practice a step higher, the coefficients are rendered in positive and negative integers.