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Common Core Math8th GradeExpressions & Equations

8.EE.7: Solve Linear Equations in One Variable

Also written as 8.EE.C.7 and CCSS.MATH.CONTENT.8.EE.C.7 · Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.

Make an 8.EE.7 WorksheetAll 28 8th Grade Math Standards

The Official Wording

Solve linear equations in one variable.

Common Core State Standards, Grade 8, Expressions & Equations · Read it at the source · Checked October 14, 2026

What 8.EE.7 Means in Plain English

Eighth graders solve equations with the variable on both sides, distributing and combining like terms first: 2(x + 3) = 5x - 6 becomes 2x + 6 = 5x - 6, so 12 = 3x and x = 4. Coefficients may be fractions or decimals.

Part a adds the other outcomes: simplifying 2x + 3 = 2x + 7 ends at 3 = 7, so no number works, while ending at 4 = 4 means every number does. High school solves the same equations with letters as coefficients (HSA-REI.3).

8.EE.7 I Can Statements

  • I can solve equations with variables on both sides.
  • I can distribute and combine like terms before solving.
  • I can tell when an equation has one, no or infinitely many solutions.

8.EE.7 Worked Example

One equation that needs the distributive property, then two small changes that give no solution and infinitely many.

Problem

Solve (1/2)(6x - 8) + 2x = 3(x + 2). Then say what happens if the right side is changed to 5x + 6, or to 5x - 4.

Solving (1/2)(6x - 8) + 2x = 3(x + 2)
  1. Distribute on both sides. Half of 6x is 3x and half of -8 is -4; 3 times x + 2 is 3x + 6.3x - 4 + 2x = 3x + 6
  2. Collect like terms on the left.5x - 4 = 3x + 6
  3. Subtract 3x from both sides to get the variable on one side, then add 4 to both sides.2x - 4 = 6, so 2x = 10
  4. Divide both sides by 2. The equation has reached the form x = a: one solution.x = 5
  5. With 5x + 6 on the right, subtracting 5x from both sides leaves a false statement.5x - 4 = 5x + 6 becomes -4 = 6: no solution
  6. With 5x - 4 on the right, the two sides are identical, so every x makes it true.5x - 4 = 5x - 4 becomes -4 = -4: infinitely many solutions
Answerx = 5. With 5x + 6 on the right there is no solution; with 5x - 4 every number is a solution.

Check it: Substitute x = 5 into the original: (1/2)(30 - 8) + 10 = 11 + 10 = 21, and 3(5 + 2) = 21. Both sides match.

Common Mistakes with 8.EE.7

Distributing to the first term only

3(x + 2) = 3x + 2

Try this: Draw arrows from the 3 to each term inside the parentheses, so 3(x + 2) becomes 3x + 6.

Reading 0 = 0 as x = 0

“5x - 4 = 5x - 4 gives 0 = 0, so x = 0.”

Try this: Read what is left: no x remains and the statement is true, so every value of x is a solution.

Dropping the sign when subtracting a group

5x - (x - 9) = 4x - 9

Try this: Rewrite the minus as -1 times the group: -(x - 9) = -x + 9, so the result is 4x + 9.

Where 8.EE.7 Fits

Comes Before7.EE.4Solve two-step equations like px + q = r and p(x + q) = r.7.EE.1Expand and combine linear expressions with rational coefficients.
Alongside8.EE.8Solve pairs of linear equations, which ends in a one-variable equation like these.
Comes Next
HSA-REI.3Solve linear equations and inequalities, including ones with letters as coefficients.
HSA-REI.1Explain each step of solving an equation as a reasoned argument.

Practice 8.EE.7

Math Worksheet GeneratorFree ToolMulti-step equations with parentheses, fractions and variables on both sides, mixed with a few that have no solution or infinitely many, answer key attached.Multi-step equationsVariables on both sidesAnswer key
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Word Problem GeneratorFree ToolStories that set two expressions equal, like two gym memberships costing the same, so writing the equation is part of the work.EquationsGrade 8
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Quick Check

  1. Solve 4(x - 3) = 2x + 6.
  2. How many solutions does 3(2x + 1) = 6x + 3 have?
  3. Solve (2/3)x - 1 = (1/3)x + 4.

8.EE.7: Other Names

8.EE.78.EE.C.7CCSS.MATH.CONTENT.8.EE.C.7

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.