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Equations with variables on both sides worksheet

Grade 8 math, Common Core 8.EE.C.7b. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Equations with variables on both sides

Grade 8 math, Common Core 8.EE.C.7b

Solve each equation. Show your work.

  1. 1.
    2(n − 2) = 3n − 3
  2. 2.
    2n − 8 = −3n + 7
  3. 3.
    3(n + 5) = 2n + 16
  4. 4.
    8n − 7 = 5n + 29
  5. 5.
    5n − 8 = 3n + 4
  6. 6.
    9n − 14 = −5n − 98
  7. 7.
    −7x + 15 = −9x + 11
  8. 8.
    5x + 2 = x + 6
  9. 9.
    −7n − 6 = 8n − 51
  10. 10.
    3(x + 2) = x − 6
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Equations with variables on both sides

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. n = −1

    2n − 4 = 3n − 3−n = 1n = −1

  2. 2. n = 3

    5n − 8 = 75n = 15n = 3

  3. 3. n = 1

    3n + 15 = 2n + 16n = 1n = 1

  4. 4. n = 12

    3n − 7 = 293n = 36n = 12

  5. 5. n = 6

    2n − 8 = 42n = 12n = 6

  6. 6. n = −6

    14n − 14 = −9814n = −84n = −6

  7. 7. x = −2

    2x + 15 = 112x = −4x = −2

  8. 8. x = 1

    4x + 2 = 64x = 4x = 1

  9. 9. n = 3

    −15n − 6 = −51−15n = −45n = 3

  10. 10. x = −6

    3x + 6 = x − 62x = −12x = −6

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About equations with variables on both sides

When the variable appears on both sides, first move all the variable terms to one side by adding or subtracting, then move the numbers to the other side, and finally divide. Moving the smaller variable term usually keeps the numbers positive.

Worked example 1

4(n − 1) = 5n + 4
  1. Step 1.4n − 4 = 5n + 4
  2. Step 2.−n = 8
  3. Step 3.n = −8

Answer: n = −8

Worked example 2

−3y − 13 = −y − 19
  1. Step 1.−2y − 13 = −19
  2. Step 2.−2y = −6
  3. Step 3.y = 3

Answer: y = 3

Worked example 3

2(n + 1) = 4n − 14
  1. Step 1.2n + 2 = 4n − 14
  2. Step 2.−2n = −16
  3. Step 3.n = 8

Answer: n = 8

Watch out for

  • Subtract the smaller variable term from both sides first.
  • Simplify each side (brackets, like terms) before moving terms across.
  • Check by putting the answer into both sides: they should be equal.

Practice equations with variables on both sides online

On StudyWiz, your kid can practice equations with variables on both sides with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

More grade 8 math worksheets

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