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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 20

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 20
Name:Date:Score:    / 12

Solve.

  1. n + 3 = 28
  2. m − 17 = 6
  3. y − 5 = 17
  4. y + 23 = 24
  5. m − 23 = 1
  6. x + 12 = 40
  7. x + 16 = 41
  8. 17 + p = 47
  9. 28 + m = 30
  10. x − 20 = 9
  11. p + 18 = 43
  12. 4 + y = 8

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 20
Name:Date:Score:    / 12

Solve.

  1. x/7 = 3
  2. m/7 = 2
  3. p/5 = 14
  4. 9n = 54
  5. p/8 = 14
  6. 2m = 12
  7. 7y = 70
  8. 6n = 66
  9. x/6 = 12
  10. y/5 = 7
  11. 7x = 91
  12. p/4 = 4

Two-step equations

Class 7 · Worksheet 3 · set 20
Name:Date:Score:    / 12

Solve.

  1. 9m − 13 = 41
  2. 4y + 19 = 63
  3. 5n − 6 = 44
  4. 3x − 16 = 17
  5. 5y + 5 = 15
  6. 5n − 9 = 16
  7. 5p + 12 = 52
  8. 7x − 16 = 26
  9. 9n + 4 = 22
  10. 8y + 11 = 83
  11. 6m + 6 = 72
  12. 6x − 12 = 42

Equations with brackets

Class 7–8 · Worksheet 4 · set 20
Name:Date:Score:    / 10

Solve.

  1. 3(y − 3) + 12 = 33
  2. 5(y − 7) + 8 = 28
  3. 3(y + 7) = 54
  4. 5(m − 1) + 2 = 37
  5. 6(m − 3) + 11 = 23
  6. 4(x + 9) = 52
  7. 4(y − 1) + 8 = 28
  8. 4(m + 8) = 72
  9. 2(y + 2) = 20
  10. 3(x − 9) + 15 = 24

Variables on both sides

Class 8 · Worksheet 5 · set 20
Name:Date:Score:    / 10

Solve.

  1. 6x − 16 = 3x + 8
  2. 3x + 3 = x − 15
  3. 6y + 15 = 5y + 12
  4. 9m + 4 = 7m + 14
  5. 8n − 16 = 7n − 18
  6. 3n + 12 = 2n + 4
  7. 4m − 12 = 3m − 20
  8. 5y − 8 = y + 20
  9. 5m − 20 = 4m − 25
  10. 7x + 1 = 6x + 5

Equation word problems

Class 7–8 · Worksheet 6 · set 20
Name:Date:Score:    / 6

Form an equation and solve.

  1. I think of a number, multiply it by 5 and add 12. The answer is 102. What is the number?
  2. The sum of two consecutive numbers is 67. Find the numbers.
  3. I think of a number, multiply it by 3 and add 4. The answer is 19. What is the number?
  4. The sum of two consecutive numbers is 35. Find the numbers.
  5. A father is 3 times as old as his son. The sum of their ages is 60 years. Find their ages.
  6. A father is 5 times as old as his son. The sum of their ages is 36 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).

How do I print only one worksheet?

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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.