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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 79

Linear equations worksheets — simple equations, Class 6 to 8

Free linear equations in one variable worksheets: one-step and two-step simple equations (Class 6–7), variables on both sides and brackets (Class 8), and word problems — with answers.

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One-step equations (+ and −) (Class 6)One-step equations (× and ÷) (Class 6–7)Two-step equations (Class 7)Equations with brackets (Class 7–8)Variables on both sides (Class 8)Equation word problems (Class 7–8)

One-step equations (+ and −)

Class 6 · Worksheet 1 · set 79
Name:Date:Score:    / 12

Solve.

  1. n + 20 = 38
  2. p + 2 = 11
  3. p − 7 = 19
  4. x + 24 = 45
  5. p + 20 = 26
  6. y + 10 = 35
  7. 27 + m = 54
  8. x + 15 = 20
  9. 29 + p = 54
  10. p + 19 = 46
  11. n − 18 = 8
  12. 11 + p = 26

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 79
Name:Date:Score:    / 12

Solve.

  1. 2p = 26
  2. y/9 = 9
  3. y/3 = 15
  4. 8p = 8
  5. y/8 = 13
  6. x/8 = 3
  7. 7n = 14
  8. x/7 = 5
  9. p/4 = 13
  10. 8p = 80
  11. n/8 = 7
  12. n/3 = 2

Two-step equations

Class 7 · Worksheet 3 · set 79
Name:Date:Score:    / 12

Solve.

  1. 9n + 18 = 99
  2. 9y + 13 = 67
  3. 7p + 8 = 78
  4. 6y − 4 = 38
  5. 6n − 11 = 25
  6. 4p + 17 = 57
  7. 4m + 4 = 44
  8. 6p + 17 = 83
  9. 6y − 3 = 69
  10. 7p − 3 = 74
  11. 9n + 13 = 67
  12. 6n − 18 = 36

Equations with brackets

Class 7–8 · Worksheet 4 · set 79
Name:Date:Score:    / 10

Solve.

  1. 4(m − 8) + 13 = 29
  2. 5(n − 4) + 1 = −9
  3. 2(n + 9) = 42
  4. 5(x − 3) + 14 = 24
  5. 2(x + 9) = 36
  6. 2(m + 7) = 38
  7. 5(m − 6) + 14 = 9
  8. 6(m − 2) + 3 = 3
  9. 3(n − 7) + 5 = 2
  10. 3(y − 7) + 15 = 18

Variables on both sides

Class 8 · Worksheet 5 · set 79
Name:Date:Score:    / 10

Solve.

  1. 7n − 3 = 5n − 19
  2. 6n − 7 = 2n − 11
  3. 3n − 6 = n − 4
  4. 3m − 17 = m − 31
  5. 5y − 18 = 4y − 9
  6. 5m − 3 = 2m + 24
  7. 7y + 14 = 6y + 7
  8. 3x − 14 = 2x − 20
  9. 8n + 19 = 7n + 28
  10. 5x − 6 = 2x − 12

Equation word problems

Class 7–8 · Worksheet 6 · set 79
Name:Date:Score:    / 6

Form an equation and solve.

  1. The length of a rectangle is 3 cm more than its width. Its perimeter is 34 cm. Find the length and the width.
  2. The length of a rectangle is 8 cm more than its width. Its perimeter is 48 cm. Find the length and the width.
  3. The length of a rectangle is 6 cm more than its width. Its perimeter is 84 cm. Find the length and the width.
  4. The length of a rectangle is 5 cm more than its width. Its perimeter is 42 cm. Find the length and the width.
  5. I think of a number, multiply it by 3 and add 19. The answer is 43. What is the number?
  6. I think of a number, multiply it by 4 and add 9. The answer is 65. What is the number?

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Questions

What is a linear equation in one variable?

An equation with one letter whose highest power is 1, such as 3x + 4 = 19. It has exactly one solution.

How do I solve word problems on simple equations?

Call the unknown x, write the sentence as an equation (“3 times a number plus 5 is 26” → 3x + 5 = 26), solve it, then check the answer in the story.

Are these worksheets free?

Yes — print them or save as PDF free. Every worksheet has an answer key.

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Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).

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Can my child do this worksheet online, like a quiz?

Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.