Solving Linear Equations Worksheet: Mixed Review for Grade 8

Print every form of linear equation mixed on one sheet, like a unit test, with its key.

20 problems. Mixed review: one step to brackets. Sheet 28715V, with its answer key.

Mixed review: one step to brackets

Name Date Score / 20

Solve each equation.

  1. 1.12x = 36  x = _____
  2. 2.n + 1 = 6  n = _____
  3. 3.y5 + 3 = 17  y = _____
  4. 4.10x − 22 = 148  x = _____
  5. 5.8n + 27 = 35  n = _____
  6. 6.2(y + 27) = 82  y = _____
  7. 7.12x = 60  x = _____
  8. 8.n + 6 = 8  n = _____
  9. 9.y7 + 1 = 12  y = _____
  10. 10.6x − 20 = 64  x = _____
  11. 11.10n + 28 = 148  n = _____
  12. 12.7(y + 14) = 105  y = _____
  13. 13.5x = 70  x = _____
  14. 14.n + 8 = 10  n = _____
  15. 15.y8 + 15 = 16  y = _____
  16. 16.11x − 6 = 27  x = _____
  17. 17.11n + 22 = 154  n = _____
  18. 18.5(y + 10) = 110  y = _____
  19. 19.5x = 90  x = _____
  20. 20.n + 3 = 6  n = _____

Sheet 28715V · Made at homeroomtools.com

Answer key. Mixed review: one step to brackets

  1. 1.12x = 36  x = 3 36 ÷ 12 = 3 Check: 12 × 3 = 36
  2. 2.n + 1 = 6  n = 5 6 − 1 = 5 Check: 5 + 1 = 6
  3. 3.y5 + 3 = 17  y = 70 17 − 3 = 14 14 × 5 = 70 Check: 70 ÷ 5 + 3 = 17
  4. 4.10x − 22 = 148  x = 17 148 + 22 = 170 170 ÷ 10 = 17 Check: 10 × 17 − 22 = 148
  5. 5.8n + 27 = 35  n = 1 35 − 27 = 8 8 ÷ 8 = 1 Check: 8 × 1 + 27 = 35
  6. 6.2(y + 27) = 82  y = 14 82 ÷ 2 = 41 41 − 27 = 14 Check: 2 × (14 + 27) = 82
  7. 7.12x = 60  x = 5 60 ÷ 12 = 5 Check: 12 × 5 = 60
  8. 8.n + 6 = 8  n = 2 8 − 6 = 2 Check: 2 + 6 = 8
  9. 9.y7 + 1 = 12  y = 77 12 − 1 = 11 11 × 7 = 77 Check: 77 ÷ 7 + 1 = 12
  10. 10.6x − 20 = 64  x = 14 64 + 20 = 84 84 ÷ 6 = 14 Check: 6 × 14 − 20 = 64
  11. 11.10n + 28 = 148  n = 12 148 − 28 = 120 120 ÷ 10 = 12 Check: 10 × 12 + 28 = 148
  12. 12.7(y + 14) = 105  y = 1 105 ÷ 7 = 15 15 − 14 = 1 Check: 7 × (1 + 14) = 105
  13. 13.5x = 70  x = 14 70 ÷ 5 = 14 Check: 5 × 14 = 70
  14. 14.n + 8 = 10  n = 2 10 − 8 = 2 Check: 2 + 8 = 10
  15. 15.y8 + 15 = 16  y = 8 16 − 15 = 1 1 × 8 = 8 Check: 8 ÷ 8 + 15 = 16
  16. 16.11x − 6 = 27  x = 3 27 + 6 = 33 33 ÷ 11 = 3 Check: 11 × 3 − 6 = 27
  17. 17.11n + 22 = 154  n = 12 154 − 22 = 132 132 ÷ 11 = 12 Check: 11 × 12 + 22 = 154
  18. 18.5(y + 10) = 110  y = 12 110 ÷ 5 = 22 22 − 10 = 12 Check: 5 × (12 + 10) = 110
  19. 19.5x = 90  x = 18 90 ÷ 5 = 18 Check: 5 × 18 = 90
  20. 20.n + 3 = 6  n = 3 6 − 3 = 3 Check: 3 + 3 = 6

Sheet 28715V · Made at homeroomtools.com

Next step Drill one two-step formAll equation worksheets

How it works

The review before a unit test: forms are shuffled, so pupils choose each first move. A free sheet mixes x + 5 = 11, 7x + 3 = 45 and 5(x + 2) = 35.

Read the full guide

Linear equation in one variable worksheet

Every problem has one letter, never squared, so each is a linear equation in one variable. Mixed review: one step to brackets keeps the letter on one side. Both sides, every form mixed puts it on both, as in 4(x − 3) = 2x + 6.

One answer, none, or every number

Common Core 8.EE.C.7a asks pupils to tell the three cases apart. One solution, no solution or infinitely many mixes them: 3x − 2 = 3x + 12 has no solution, and 2(x + 1) = 2x + 2 holds for every number.

  • Before solving, ask pupils to label each problem 1, 2 or both sides. Choosing the method is what a mixed sheet tests.
  • Print the single-form pages first; this page is for the week before the test.

Questions and answers

What makes an equation linear?

The letter appears only to the first power and is never multiplied by itself or divided into a number. 7x + 3 = 45 is linear; x² = 49 and 12/x = 3 are not.

Can one sheet mix x on one side with x on both sides?

Not yet. The one-side sheets mix one-step, two-step and bracket forms; the both-sides sheets mix ax + b = cx + d with one or two brackets. Print one of each for a full review.

Does the key show the working?

Yes. One-side sheets print each undoing step and a check; both-sides sheets print the expanded line, the collected line and the division, such as 2x = 18, then 18 ÷ 2 = 9.

All 9 sheet types

Mixed forms, the letter on one side 3

  • Mixed review with fractions and decimals 3/4x + 2 = 8, 1.5x − 2 = 7 and 2/3(x + 4) = 10 among whole-number equations; every answer is whole.
  • Mixed review with negative numbers x − 7 = −12, −6x = 42, −3x + 8 = 29 and −2(x − 4) = 18 on one sheet, answers from −12 to 12.
  • Mixed review: one step to brackets x + 5 = 11, 4x = 20, 7x + 3 = 45, x/3 + 2 = 9 and 5(x + 2) = 35 shuffled, whole numbers only; the key writes each undoing line.

Mixed forms, the letter on both sides 4

  • Both sides with negatives, every form mixed −2x − 16 = −3x − 18, −3(x − 7) = x + 9 and 4(x + 9) = −4(x + 3), answers from −12 to 12.
  • Both sides, every form mixed 6x + 4 = x + 24, 4(x − 3) = 2x + 6 and 3(x + 10) = 6(x + 1) on one sheet, whole-number answers.
  • One solution, no solution or infinitely many 3x − 2 = 3x + 12 has no solution; 2(x + 1) = 2x + 2 is true for every number, which the key writes as all real numbers; the rest have one answer.
  • Rational answers, every form mixed 6x − 11 = 3x − 1 gives x = 10/3 and 2(x + 5) = 8x − 5 gives x = 5/2; about one answer in six is whole.

Checks and quick review 2

  • Quick review: 30 equations across 30 one- and two-step equations in rows, such as x + 2 = 8 and 10x − 9 = 31, for a warm-up or a timed review.
  • Solve and check, one and two steps A work line and a Check line under 5x − 16 = 59, x/6 = 5 or 7(x + 13) = 112; the key fills in 7 × (3 + 13) = 112.

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