Multi Step Equations Worksheets: Like Terms, Brackets, Both Sides

Print equations like 3x + 4 + 2x = 29 that take three moves, with every step on the key.

12 problems. Combine like terms: 3x + 4 + 2x = 29. Sheet 52O0VQ, with its answer key.

Combine like terms: 3x + 4 + 2x = 29

Name Date Score / 12

Solve each equation. Show each step.

  1. 1.n + 17 + 8n = 98n = _____
  2. 2.5x + 5 + x = 71x = _____
  3. 3.9y + 8 + 5y = 78y = _____
  4. 4.2n + 13 + 5n = 55n = _____
  5. 5.4x + 18 + 6x = 98x = _____
  6. 6.2y + 19 + y = 43y = _____
  7. 7.9n + 16 + 8n = 118n = _____
  8. 8.3x + 4 + 6x = 49x = _____
  9. 9.5y + 15 + 6y = 26y = _____
  10. 10.9n + 4 + 6n = 139n = _____
  11. 11.x + 19 + 3x = 35x = _____
  12. 12.3y + 10 + 5y = 34y = _____

Sheet 52O0VQ · Made at homeroomtools.com

Answer key. Combine like terms: 3x + 4 + 2x = 29

  1. 1.n + 17 + 8n = 98 9n + 17 = 98 9n = 81 81 ÷ 9 = 9 Check: 9 + 17 + 8 × 9 = 98n = 9
  2. 2.5x + 5 + x = 71 6x + 5 = 71 6x = 66 66 ÷ 6 = 11 Check: 5 × 11 + 5 + 11 = 71x = 11
  3. 3.9y + 8 + 5y = 78 14y + 8 = 78 14y = 70 70 ÷ 14 = 5 Check: 9 × 5 + 8 + 5 × 5 = 78y = 5
  4. 4.2n + 13 + 5n = 55 7n + 13 = 55 7n = 42 42 ÷ 7 = 6 Check: 2 × 6 + 13 + 5 × 6 = 55n = 6
  5. 5.4x + 18 + 6x = 98 10x + 18 = 98 10x = 80 80 ÷ 10 = 8 Check: 4 × 8 + 18 + 6 × 8 = 98x = 8
  6. 6.2y + 19 + y = 43 3y + 19 = 43 3y = 24 24 ÷ 3 = 8 Check: 2 × 8 + 19 + 8 = 43y = 8
  7. 7.9n + 16 + 8n = 118 17n + 16 = 118 17n = 102 102 ÷ 17 = 6 Check: 9 × 6 + 16 + 8 × 6 = 118n = 6
  8. 8.3x + 4 + 6x = 49 9x + 4 = 49 9x = 45 45 ÷ 9 = 5 Check: 3 × 5 + 4 + 6 × 5 = 49x = 5
  9. 9.5y + 15 + 6y = 26 11y + 15 = 26 11y = 11 11 ÷ 11 = 1 Check: 5 × 1 + 15 + 6 × 1 = 26y = 1
  10. 10.9n + 4 + 6n = 139 15n + 4 = 139 15n = 135 135 ÷ 15 = 9 Check: 9 × 9 + 4 + 6 × 9 = 139n = 9
  11. 11.x + 19 + 3x = 35 4x + 19 = 35 4x = 16 16 ÷ 4 = 4 Check: 4 + 19 + 3 × 4 = 35x = 4
  12. 12.3y + 10 + 5y = 34 8y + 10 = 34 8y = 24 24 ÷ 8 = 3 Check: 3 × 3 + 10 + 5 × 3 = 34y = 3

Sheet 52O0VQ · Made at homeroomtools.com

Next step Review two-step equationsNext: x on both sides

How it works

Each equation takes three moves or more. A free sheet has 12 like 3x + 4 + 2x = 29; Sheet type adds negatives, a bracket before the like terms, x on both sides and a mixed review.

Read the full guide

Combining like terms and solving equations worksheet

Tidy each side first. 3x + 4 + 2x = 29 has two x terms: 3x + 2x = 5x, so 5x + 4 = 29. Then it is a two-step equation: 5x = 25, x = 5. With a bracket, as in 2(x + 3) + x = 18, expand first: 2x + 6 + x = 18.

Solving multi step equations worksheet order

Print Combine like terms: 3x + 4 + 2x = 29, then A bracket, then like terms: 2(x + 3) + x = 18, then negatives. Multi-step review: like terms and x on both sides is the 3 step equations worksheet for the week before a test.

  • Have pupils circle the x terms before solving: in 3x + 4 + 2x = 29, the 3x and the 2x.
  • Common Core 8.EE.C.7b names both skills: expanding with the distributive property and collecting like terms.

Questions and answers

Can I get multi step equations worksheets as a PDF?

Yes. Press Print and choose Save as PDF as the printer. The answer key, with every combined line and division, prints on its own page after the sheet; untick Answer key to leave it out.

What does the key show?

Each step on its own line: the expanded bracket, the combined line (5x + 4 = 29), the line after the constant moves (5x = 25), the division and the answer. Most sheets add a check with the answer put back in.

Are the answers whole numbers?

Yes, on all 9 sheet types, and never 0. Answers run from −10 to 12; the sheets with negatives in the title have negative answers about half the time.

All 9 sheet types

Combine like terms 2

  • Combine like terms: 3x + 4 + 2x = 29 3x + 4 + 2x = 29: combine to 5x + 4 = 29, then 5x = 25 and x = 5. Every number printed is positive.
  • Like terms with negatives: 7x − 5 − 3x = 23 7x − 5 − 3x = 23: combine to 4x − 5 = 23, then 4x = 28 and x = 7. Coefficients from −9 to 9, answers from −10 to 10.

A bracket, then like terms 3

  • A bracket and negatives: −3(x − 2) + 5x = 14 −3(x − 2) + 5x = 14: expand to −3x + 6 + 5x = 14, combine to 2x + 6 = 14, so x = 4.
  • A bracket, then like terms: 2(x + 3) + x = 18 2(x + 3) + x = 18: expand to 2x + 6 + x = 18, combine to 3x + 6 = 18, so 3x = 12 and x = 4.
  • Like terms with and without a bracket 3x + 4 + 2x = 29 and 2(x + 3) + x = 18 shuffled on one sheet, so each problem starts with a choice: expand or combine.

Multi-step review and checks 4

  • Combine, solve, then check A work line and a Check line under each like-terms equation; for 3x + 4 + 2x = 29 the key checks 3 × 5 + 4 + 2 × 5 = 29.
  • Multi-step review: like terms and x on both sides 3x + 4 + 2x = 29, 2(x + 3) + x = 18, 5x − 3 = 2x + 9 and 4(x − 3) = 2x + 6 on one sheet: the unit review.
  • Multi-step with x on both sides: 5x − 3 = 2x + 9 5x − 3 = 2x + 9: take 2x from both sides, 3x − 3 = 9, so 3x = 12 and x = 4. Some sheets start with a bracket.
  • Quick sheet: 20 like-term equations across 20 short equations such as 4x + 7 + x = 32 in rows, for a warm-up; the key gives each answer.

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