StudyWiz home
Sign inStart free

Linear equations worksheet

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

NameDate

Linear equations

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

Solve each equation. If it has no solution or infinitely many, say so.

  1. 1.
    0.25x + 6 = 7
  2. 2.
    x4 + x6 = 5
  3. 3.
    x2 + x3 = 20
  4. 4.
    x4 + x6 = 15
  5. 5.
    0.25x − 5 = −2
  6. 6.
    5(x + 5) + 4x = −47
  7. 7.
    3(x − 4) = 3x − 8
  8. 8.
    1.5x − 8 = 7
  9. 9.
    x2 + x5 = 28
  10. 10.
    3(x + 3) + 5x = 81
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Linear equations

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

  1. 1. x = 4

    0.25x = 1x = 1 ÷ 0.25 = 4

  2. 2. x = 12

    Multiply every term by 12: 3x + 2x = 605x = 60x = 12

  3. 3. x = 24

    Multiply every term by 6: 3x + 2x = 1205x = 120x = 24

  4. 4. x = 36

    Multiply every term by 12: 3x + 2x = 1805x = 180x = 36

  5. 5. x = 12

    0.25x = 3x = 3 ÷ 0.25 = 12

  6. 6. x = −8

    5x + 25 + 4x = −479x + 25 = −47x = −8

  7. 7. No solution

    3x − 12 = 3x − 8−12 = −8 is false

  8. 8. x = 10

    1.5x = 15x = 15 ÷ 1.5 = 10

  9. 9. x = 40

    Multiply every term by 10: 5x + 2x = 2807x = 280x = 40

  10. 10. x = 9

    3x + 9 + 5x = 818x + 9 = 81x = 9

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

About linear equations

To solve a multi-step linear equation, simplify each side first (use the distributive property and combine like terms), then use inverse operations to get the variable alone. Some equations have exactly one solution, some have none (they simplify to something false like 4 = −1) and some have infinitely many (they simplify to something always true like 6 = 6).

Worked example 1

0.5x + 9 = 18
  1. Step 1.0.5x = 9
  2. Step 2.x = 9 ÷ 0.5 = 18

Answer: x = 18

Worked example 2

5(x − 1) = 5x − 10
  1. Step 1.5x − 5 = 5x − 10
  2. Step 2.−5 = −10 is false

Answer: No solution

Worked example 3

5(x − 2) = 5x − 7
  1. Step 1.5x − 10 = 5x − 7
  2. Step 2.−10 = −7 is false

Answer: No solution

Watch out for

  • Clear brackets first, then combine like terms on each side.
  • To clear fractions, multiply every term by the common denominator.
  • If the variables cancel out, check whether what is left is true (infinitely many solutions) or false (no solution).

Practice linear equations online

On StudyWiz, your kid can practice linear equations 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

More from Expressions and equations:

Other grade 8 topics:

See all 8th grade math worksheets, or switch to grade 6 or grade 7.

Keep reading

Try Wiz with tonight’s homework

Free to start, no card needed. Each kid gets 3 homework questions, 5 practice quizzes and 1 writing review a day on the free plan.

Start freeSee pricing