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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 29

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 29
Name:Date:Score:    / 12

Solve.

  1. n + 15 = 32
  2. 3 + y = 13
  3. 27 + x = 28
  4. 27 + y = 32
  5. m + 18 = 28
  6. n + 10 = 39
  7. 24 + n = 46
  8. 13 + m = 42
  9. m + 14 = 31
  10. y + 29 = 50
  11. 23 + n = 34
  12. n + 23 = 32

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 29
Name:Date:Score:    / 12

Solve.

  1. p/6 = 8
  2. n/6 = 11
  3. 3n = 42
  4. 2y = 28
  5. p/5 = 11
  6. 9y = 135
  7. x/3 = 14
  8. 7n = 49
  9. p/4 = 15
  10. p/3 = 7
  11. 4x = 36
  12. 5n = 5

Two-step equations

Class 7 · Worksheet 3 · set 29
Name:Date:Score:    / 12

Solve.

  1. 2p + 13 = 19
  2. 9y + 8 = 17
  3. 7p + 6 = 20
  4. 3y + 13 = 22
  5. 9n − 16 = 74
  6. 8n − 8 = 24
  7. 9x + 3 = 66
  8. 6x + 11 = 17
  9. 5x + 19 = 64
  10. 5p − 6 = 49
  11. 3m + 1 = 16
  12. 7m − 16 = 47

Equations with brackets

Class 7–8 · Worksheet 4 · set 29
Name:Date:Score:    / 10

Solve.

  1. 5(m − 4) + 6 = 21
  2. 5(y + 4) = 30
  3. 3(x − 6) + 9 = 9
  4. 5(y + 3) = 25
  5. 4(m − 7) + 9 = −3
  6. 5(n + 5) = 70
  7. 3(n − 9) + 5 = −4
  8. 4(x − 4) + 10 = 26
  9. 6(n + 5) = 78
  10. 2(y − 2) + 12 = 26

Variables on both sides

Class 8 · Worksheet 5 · set 29
Name:Date:Score:    / 10

Solve.

  1. 6n + 9 = n − 11
  2. 7m + 15 = 5m + 7
  3. 6y + 13 = 2y − 3
  4. 8y − 5 = y − 19
  5. 4n − 20 = 2n − 4
  6. 4n + 19 = 3n + 17
  7. 8n + 19 = 7n + 21
  8. 3x − 9 = x − 25
  9. 8x + 8 = 6x + 18
  10. 5x − 1 = 4x + 8

Equation word problems

Class 7–8 · Worksheet 6 · set 29
Name:Date:Score:    / 6

Form an equation and solve.

  1. The sum of two consecutive numbers is 75. Find the numbers.
  2. I think of a number, multiply it by 5 and add 1. The answer is 16. What is the number?
  3. A father is 3 times as old as his son. The sum of their ages is 28 years. Find their ages.
  4. I think of a number, multiply it by 4 and add 10. The answer is 66. What is the number?
  5. The sum of two consecutive numbers is 37. Find the numbers.
  6. I think of a number, multiply it by 2 and add 4. The answer is 8. 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.