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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 36

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 36
Name:Date:Score:    / 12

Solve.

  1. x + 24 = 39
  2. 4 + m = 8
  3. x + 25 = 30
  4. 6 + y = 33
  5. 16 + x = 18
  6. x + 14 = 18
  7. y + 9 = 36
  8. y + 1 = 18
  9. 8 + x = 34
  10. 19 + m = 23
  11. n − 12 = 15
  12. 4 + m = 34

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 36
Name:Date:Score:    / 12

Solve.

  1. 9p = 72
  2. 6p = 90
  3. 7x = 56
  4. x/3 = 1
  5. n/8 = 14
  6. 7m = 35
  7. 6m = 54
  8. 5x = 60
  9. 6x = 12
  10. 9p = 117
  11. y/4 = 1
  12. m/9 = 3

Two-step equations

Class 7 · Worksheet 3 · set 36
Name:Date:Score:    / 12

Solve.

  1. 5n + 13 = 38
  2. 9n − 13 = 95
  3. 6n + 3 = 27
  4. 3x + 16 = 19
  5. 4p + 13 = 17
  6. 6n + 15 = 51
  7. 5p + 5 = 30
  8. 4x − 5 = 39
  9. 3m + 20 = 38
  10. 4p + 20 = 44
  11. 3x + 11 = 17
  12. 8m − 7 = 41

Equations with brackets

Class 7–8 · Worksheet 4 · set 36
Name:Date:Score:    / 10

Solve.

  1. 2(x + 3) = 8
  2. 5(m + 4) = 70
  3. 2(m + 8) = 28
  4. 3(x − 1) + 13 = 37
  5. 5(y − 6) + 7 = −8
  6. 6(x + 3) = 36
  7. 2(y − 2) + 5 = 21
  8. 6(x + 9) = 120
  9. 4(y − 6) + 3 = 3
  10. 5(x + 9) = 70

Variables on both sides

Class 8 · Worksheet 5 · set 36
Name:Date:Score:    / 10

Solve.

  1. 6x + 4 = x + 34
  2. 8n + 10 = 7n + 16
  3. 9y − 6 = 7y − 4
  4. 8y + 9 = 2y + 33
  5. 3n − 9 = n + 7
  6. 9y − 4 = y − 28
  7. 5y − 19 = 4y − 21
  8. 5x + 13 = 3x − 5
  9. 7y − 7 = 5y + 1
  10. 9x + 5 = 4x + 35

Equation word problems

Class 7–8 · Worksheet 6 · set 36
Name:Date:Score:    / 6

Form an equation and solve.

  1. I think of a number, multiply it by 6 and add 3. The answer is 51. What is the number?
  2. A father is 3 times as old as his son. The sum of their ages is 28 years. Find their ages.
  3. I think of a number, multiply it by 2 and add 7. The answer is 11. What is the number?
  4. I think of a number, multiply it by 5 and add 10. The answer is 20. What is the number?
  5. A father is 5 times as old as his son. The sum of their ages is 54 years. Find their ages.
  6. The length of a rectangle is 8 cm more than its width. Its perimeter is 68 cm. Find the length and the width.

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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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Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.

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.