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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 2

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 2
Name:Date:Score:    / 12

Solve.

  1. 12 + p = 22
  2. 20 + m = 40
  3. m + 26 = 37
  4. 29 + n = 43
  5. 8 + y = 10
  6. 13 + m = 31
  7. x − 16 = 7
  8. x + 21 = 32
  9. n + 2 = 11
  10. 21 + n = 23
  11. m − 14 = 14
  12. m − 11 = 7

One-step equations (× and ÷)

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

Solve.

  1. m/9 = 3
  2. 4n = 48
  3. 3m = 42
  4. 4x = 40
  5. 5m = 50
  6. p/7 = 11
  7. p/2 = 7
  8. 3n = 45
  9. x/8 = 8
  10. 3m = 45
  11. n/4 = 12
  12. x/3 = 15

Two-step equations

Class 7 · Worksheet 3 · set 2
Name:Date:Score:    / 12

Solve.

  1. 2y + 14 = 30
  2. 6x − 9 = 15
  3. 5m + 20 = 25
  4. 8y + 10 = 18
  5. 8y + 8 = 24
  6. 9p − 16 = 83
  7. 2n + 7 = 17
  8. 2x + 3 = 13
  9. 8p + 6 = 54
  10. 9p + 2 = 110
  11. 8y + 17 = 89
  12. 3x − 19 = 8

Equations with brackets

Class 7–8 · Worksheet 4 · set 2
Name:Date:Score:    / 10

Solve.

  1. 2(x − 6) + 2 = −2
  2. 6(n + 6) = 72
  3. 5(y − 6) + 10 = 35
  4. 6(y − 3) + 14 = 32
  5. 2(x − 6) + 10 = 2
  6. 5(y + 7) = 95
  7. 3(y − 6) + 1 = −5
  8. 5(y − 4) + 8 = 8
  9. 5(y − 1) + 14 = 69
  10. 3(y + 9) = 45

Variables on both sides

Class 8 · Worksheet 5 · set 2
Name:Date:Score:    / 10

Solve.

  1. 4n − 20 = n − 41
  2. 4x − 3 = 2x − 1
  3. 4y + 2 = 3y − 1
  4. 3x + 11 = x + 29
  5. 5x + 8 = 3x + 14
  6. 7y − 7 = 5y + 5
  7. 6x − 16 = 2x − 32
  8. 9m − 16 = 3m − 10
  9. 8y − 9 = y + 54
  10. 7x + 3 = 6x − 4

Equation word problems

Class 7–8 · Worksheet 6 · set 2
Name:Date:Score:    / 6

Form an equation and solve.

  1. A father is 4 times as old as his son. The sum of their ages is 30 years. Find their ages.
  2. The sum of two consecutive numbers is 85. Find the numbers.
  3. The length of a rectangle is 10 cm more than its width. Its perimeter is 48 cm. Find the length and the width.
  4. The length of a rectangle is 1 cm more than its width. Its perimeter is 58 cm. Find the length and the width.
  5. A father is 4 times as old as his son. The sum of their ages is 55 years. Find their ages.
  6. The length of a rectangle is 6 cm more than its width. Its perimeter is 88 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).

How do I print only one worksheet?

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.