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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 83

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 83
Name:Date:Score:    / 12

Solve.

  1. y + 29 = 40
  2. 1 + x = 11
  3. 15 + y = 22
  4. y + 20 = 29
  5. 17 + x = 25
  6. p + 23 = 44
  7. y + 29 = 39
  8. x + 15 = 23
  9. 21 + n = 50
  10. 3 + p = 25
  11. 27 + x = 50
  12. n + 30 = 39

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 83
Name:Date:Score:    / 12

Solve.

  1. 6x = 12
  2. p/7 = 4
  3. 8y = 112
  4. p/8 = 12
  5. 9m = 72
  6. x/8 = 14
  7. 5n = 5
  8. 7p = 42
  9. 2m = 28
  10. 5x = 45
  11. 6m = 78
  12. x/6 = 6

Two-step equations

Class 7 · Worksheet 3 · set 83
Name:Date:Score:    / 12

Solve.

  1. 9x − 10 = 62
  2. 8y − 15 = 25
  3. 9m + 15 = 114
  4. 8x + 9 = 57
  5. 2x − 15 = 5
  6. 4m + 1 = 5
  7. 4n − 5 = 15
  8. 2n + 17 = 21
  9. 7y − 5 = 16
  10. 8x + 15 = 87
  11. 9m − 1 = 98
  12. 4p − 9 = 35

Equations with brackets

Class 7–8 · Worksheet 4 · set 83
Name:Date:Score:    / 10

Solve.

  1. 3(y + 4) = 48
  2. 4(y − 4) + 13 = 37
  3. 3(x + 6) = 33
  4. 4(n + 5) = 28
  5. 4(m − 8) + 11 = 23
  6. 6(y − 8) + 15 = −15
  7. 3(y + 6) = 30
  8. 3(m + 8) = 48
  9. 4(m + 2) = 48
  10. 3(n + 2) = 21

Variables on both sides

Class 8 · Worksheet 5 · set 83
Name:Date:Score:    / 10

Solve.

  1. 5y + 18 = y − 18
  2. 3n − 11 = 2n − 8
  3. 4x − 1 = 2x − 17
  4. 5x + 10 = 2x + 4
  5. 9n + 13 = 4n − 17
  6. 8x − 9 = 6x − 19
  7. 5y + 5 = 4y + 9
  8. 8x + 1 = 2x − 47
  9. 5n − 13 = 4n − 16
  10. 4n + 1 = n + 16

Equation word problems

Class 7–8 · Worksheet 6 · set 83
Name:Date:Score:    / 6

Form an equation and solve.

  1. I think of a number, multiply it by 4 and add 4. The answer is 32. What is the number?
  2. The length of a rectangle is 1 cm more than its width. Its perimeter is 82 cm. Find the length and the width.
  3. A father is 5 times as old as his son. The sum of their ages is 36 years. Find their ages.
  4. I think of a number, multiply it by 5 and add 18. The answer is 118. What is the number?
  5. I think of a number, multiply it by 5 and add 10. The answer is 40. What is the number?
  6. A father is 4 times as old as his son. The sum of their ages is 25 years. Find their ages.

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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?

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