Solving Equations With Distributive Property Worksheet, Grades 7 and 8

A bracket in every equation, like 5(x − 3) = 35, and a key that shows each step.

20 problems. One bracket equals a number: 3(x + 4) = 27. Sheet 3UZEDD, with its answer key.

One bracket equals a number: 3(x + 4) = 27

Name Date Score / 20

Solve each equation.

  1. 1.4(n + 13) = 104  n = _____
  2. 2.9(x + 7) = 126  x = _____
  3. 3.8(y + 10) = 88  y = _____
  4. 4.2(n + 11) = 54  n = _____
  5. 5.8(x + 15) = 280  x = _____
  6. 6.4(y + 5) = 28  y = _____
  7. 7.5(n + 5) = 35  n = _____
  8. 8.7(x + 11) = 84  x = _____
  9. 9.5(y + 5) = 40  y = _____
  10. 10.7(n + 9) = 189  n = _____
  11. 11.5(x + 1) = 25  x = _____
  12. 12.5(y + 3) = 70  y = _____
  13. 13.5(n + 3) = 90  n = _____
  14. 14.4(x + 8) = 88  x = _____
  15. 15.4(y + 6) = 84  y = _____
  16. 16.3(n + 9) = 30  n = _____
  17. 17.8(x + 12) = 120  x = _____
  18. 18.3(y + 9) = 78  y = _____
  19. 19.5(n + 11) = 60  n = _____
  20. 20.2(x + 9) = 26  x = _____

Sheet 3UZEDD · Made at homeroomtools.com

Answer key. One bracket equals a number: 3(x + 4) = 27

  1. 1.4(n + 13) = 104  n = 13 104 ÷ 4 = 26 26 − 13 = 13 Check: 4 × (13 + 13) = 104
  2. 2.9(x + 7) = 126  x = 7 126 ÷ 9 = 14 14 − 7 = 7 Check: 9 × (7 + 7) = 126
  3. 3.8(y + 10) = 88  y = 1 88 ÷ 8 = 11 11 − 10 = 1 Check: 8 × (1 + 10) = 88
  4. 4.2(n + 11) = 54  n = 16 54 ÷ 2 = 27 27 − 11 = 16 Check: 2 × (16 + 11) = 54
  5. 5.8(x + 15) = 280  x = 20 280 ÷ 8 = 35 35 − 15 = 20 Check: 8 × (20 + 15) = 280
  6. 6.4(y + 5) = 28  y = 2 28 ÷ 4 = 7 7 − 5 = 2 Check: 4 × (2 + 5) = 28
  7. 7.5(n + 5) = 35  n = 2 35 ÷ 5 = 7 7 − 5 = 2 Check: 5 × (2 + 5) = 35
  8. 8.7(x + 11) = 84  x = 1 84 ÷ 7 = 12 12 − 11 = 1 Check: 7 × (1 + 11) = 84
  9. 9.5(y + 5) = 40  y = 3 40 ÷ 5 = 8 8 − 5 = 3 Check: 5 × (3 + 5) = 40
  10. 10.7(n + 9) = 189  n = 18 189 ÷ 7 = 27 27 − 9 = 18 Check: 7 × (18 + 9) = 189
  11. 11.5(x + 1) = 25  x = 4 25 ÷ 5 = 5 5 − 1 = 4 Check: 5 × (4 + 1) = 25
  12. 12.5(y + 3) = 70  y = 11 70 ÷ 5 = 14 14 − 3 = 11 Check: 5 × (11 + 3) = 70
  13. 13.5(n + 3) = 90  n = 15 90 ÷ 5 = 18 18 − 3 = 15 Check: 5 × (15 + 3) = 90
  14. 14.4(x + 8) = 88  x = 14 88 ÷ 4 = 22 22 − 8 = 14 Check: 4 × (14 + 8) = 88
  15. 15.4(y + 6) = 84  y = 15 84 ÷ 4 = 21 21 − 6 = 15 Check: 4 × (15 + 6) = 84
  16. 16.3(n + 9) = 30  n = 1 30 ÷ 3 = 10 10 − 9 = 1 Check: 3 × (1 + 9) = 30
  17. 17.8(x + 12) = 120  x = 3 120 ÷ 8 = 15 15 − 12 = 3 Check: 8 × (3 + 12) = 120
  18. 18.3(y + 9) = 78  y = 17 78 ÷ 3 = 26 26 − 9 = 17 Check: 3 × (17 + 9) = 78
  19. 19.5(n + 11) = 60  n = 1 60 ÷ 5 = 12 12 − 11 = 1 Check: 5 × (1 + 11) = 60
  20. 20.2(x + 9) = 26  x = 4 26 ÷ 2 = 13 13 − 9 = 4 Check: 2 × (4 + 9) = 26

Sheet 3UZEDD · Made at homeroomtools.com

Next step Review the distributive property with numbersAll equation worksheets

How it works

Every problem has a bracket. The first sheet has 20 like 7(x + 2) = 98; Sheet type adds a minus inside, a negative, decimal or fraction outside, x on the other side, and a bracket on each side.

Read the full guide

Divide first or distribute first

7(x + 2) = 98 can go either way. Divide by 7: x + 2 = 14, so x = 12. Or distribute: 7x + 14 = 98, 7x = 84, x = 12. The key divides first on these sheets. When x is on the other side too, as in 4(x − 3) = 2x + 6, distributing is the only way.

Multi step equations with distributive property worksheet

Print Bracket against x terms: 4(x − 3) = 2x + 6 or A bracket on each side: 3(x + 2) = 5(x − 2): expand, collect, divide. The key prints the expanded line, 4x − 12 = 2x + 6, then 2x = 18.

  • The common slip is 4(x − 3) = 4x − 3. Ask pupils to draw an arrow from the 4 to each term.
  • On A negative outside the bracket, −4(x − 2) is −4x + 8: the second sign flips too.

Questions and answers

Where is the solve equations with distributive property worksheet with negatives?

Choose A negative outside the bracket for problems like −4(x − 2) = 20, or Negative outside, x on the other side for −5(x + 4) = −8x − 11, where both x terms are negative.

Are any answers fractions?

Only on Distribute, then a fraction answer, where 2(x + 5) = 8x − 5 gives x = 5/2. The decimal and fraction sheets put the decimal or fraction outside the bracket, and their answers are whole.

How do I save the equations with the distributive property worksheet as a PDF?

Press Print and choose Save as PDF as the printer. The answer key prints on its own page after the sheet; untick Answer key to leave it out.

All 11 sheet types

A bracket equals a number 5

  • A decimal outside the bracket: 1.5(x + 4) = 15 1.5(x + 4) = 15: divide by 1.5 (10), then take 4 away: x = 6. Tenths outside; every answer whole.
  • A fraction outside the bracket: 2/3(x + 4) = 10 2/3(x + 4) = 10: divide by 2/3 (15), then take 4 away: x = 11. Halves to fifths; every answer whole.
  • A minus inside the bracket: 5(x − 3) = 35 5(x − 3) = 35: divide by 5 (7), then add 3: x = 10.
  • A negative outside the bracket: −4(x − 2) = 20 −4(x − 2) = 20: divide by −4 (−5), then add 2: x = −3. Every number outside is from −9 to −2.
  • One bracket equals a number: 3(x + 4) = 27 7(x + 2) = 98: divide by 7 (14), then take 2 away: x = 12. Or expand, 7x + 14 = 98, then 7x = 84: the same 12.

A bracket and the letter on the other side 3

  • A bracket on each side: 3(x + 2) = 5(x − 2) 4(x + 4) = 2(x + 11): expand to 4x + 16 = 2x + 22, collect 2x = 6, so x = 3.
  • Bracket against x terms: 4(x − 3) = 2x + 6 4(x − 3) = 2x + 6: expand to 4x − 12 = 2x + 6, collect 2x = 18, so x = 9. Numbers outside from 2 to 9.
  • Negative outside, x on the other side −5(x + 4) = −8x − 11: expand to −5x − 20 = −8x − 11, collect 3x = 9, so x = 3. Both x terms are negative.
Show all 11 sheet types (3 more)

Fraction answers, special cases and checks 3

  • Bracket equations with no solution or every solution 2(x + 1) = 2x + 2 expands to the same both sides, so every number works; 3(x − 1) = 3x + 4 gives −3 ≠ 4, no solution. The rest have one answer.
  • Distribute, then a fraction answer 2(x + 5) = 8x − 5: expand to 2x + 10 = 8x − 5, collect −6x = −15, so x = 5/2. Halves to fifths.
  • Expand, solve, then check A work line and a Check line under each; for 6(x − 5) = 4x − 6 the key checks 6 × (12 − 5) = 42 and 4 × 12 − 6 = 42.

How this list was compiled: Our own list of sheet types, written on 2026-09-24. Every equation is made backwards from its answer in exact fractions, and a second program reads each printed equation again and solves it, 10,000 problems per sheet type. Common Core 7.EE.B.4a (solve equations of the form p(x + q) = r fluently) and 8.EE.C.7b (solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms), read on 2026-09-24 at https://tasks.illustrativemathematics.org/content-standards/7/EE/B/4 and https://tasks.illustrativemathematics.org/content-standards/8/EE/C/7 . The standards are a checklist for teachers; their authors have not reviewed these sheets. Licence: own work

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