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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 54

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 54
Name:Date:Score:    / 12

Solve.

  1. 20 + x = 21
  2. p − 7 = 1
  3. p − 16 = 9
  4. m + 18 = 27
  5. 20 + n = 50
  6. p + 2 = 5
  7. m − 24 = 1
  8. x + 26 = 27
  9. 20 + y = 49
  10. x + 29 = 49
  11. y + 10 = 40
  12. m + 29 = 49

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 54
Name:Date:Score:    / 12

Solve.

  1. 8p = 80
  2. n/3 = 6
  3. n/8 = 1
  4. x/5 = 2
  5. y/3 = 10
  6. 3x = 27
  7. x/8 = 11
  8. 4p = 32
  9. y/5 = 14
  10. m/7 = 4
  11. 8p = 64
  12. 4n = 60

Two-step equations

Class 7 · Worksheet 3 · set 54
Name:Date:Score:    / 12

Solve.

  1. 8n + 13 = 93
  2. 9m + 19 = 82
  3. 8m − 18 = 70
  4. 4y + 4 = 48
  5. 8p + 9 = 57
  6. 5x + 9 = 44
  7. 4m + 18 = 38
  8. 5n + 7 = 62
  9. 5m − 9 = 1
  10. 9x − 15 = 12
  11. 2m + 16 = 30
  12. 3y − 6 = 3

Equations with brackets

Class 7–8 · Worksheet 4 · set 54
Name:Date:Score:    / 10

Solve.

  1. 2(m − 4) + 3 = −1
  2. 5(n + 8) = 100
  3. 3(y − 2) + 11 = 8
  4. 5(y + 7) = 55
  5. 6(n + 4) = 78
  6. 4(x + 4) = 32
  7. 2(y + 3) = 12
  8. 2(n − 9) + 6 = −4
  9. 4(x − 5) + 8 = 32
  10. 5(n − 1) + 7 = 32

Variables on both sides

Class 8 · Worksheet 5 · set 54
Name:Date:Score:    / 10

Solve.

  1. 9m + 14 = m − 2
  2. 9x + 18 = 3x − 36
  3. 7m − 17 = 4m − 5
  4. 7n + 17 = 5n + 9
  5. 9y − 15 = 2y + 13
  6. 8y − 6 = y − 69
  7. 9n + 11 = 7n − 1
  8. 4m + 18 = 2m + 14
  9. 4m + 20 = m + 23
  10. 8x − 15 = 7x − 14

Equation word problems

Class 7–8 · Worksheet 6 · set 54
Name:Date:Score:    / 6

Form an equation and solve.

  1. I think of a number, multiply it by 4 and add 18. The answer is 90. What is the number?
  2. The length of a rectangle is 8 cm more than its width. Its perimeter is 32 cm. Find the length and the width.
  3. A father is 4 times as old as his son. The sum of their ages is 40 years. Find their ages.
  4. The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. Find the length and the width.
  5. The length of a rectangle is 10 cm more than its width. Its perimeter is 100 cm. Find the length and the width.
  6. I think of a number, multiply it by 5 and add 14. The answer is 99. 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.

How do I get different questions?

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.