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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 5

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 5
Name:Date:Score:    / 12

Solve.

  1. 28 + x = 50
  2. 29 + y = 41
  3. n + 2 = 30
  4. 4 + y = 18
  5. m + 17 = 46
  6. n + 1 = 13
  7. 6 + y = 8
  8. n − 2 = 4
  9. p + 8 = 12
  10. p + 9 = 24
  11. 21 + p = 22
  12. 18 + n = 38

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 5
Name:Date:Score:    / 12

Solve.

  1. p/5 = 3
  2. 2n = 14
  3. 9p = 54
  4. 4y = 40
  5. y/8 = 12
  6. 9x = 126
  7. p/2 = 9
  8. p/6 = 14
  9. 2n = 24
  10. 6p = 24
  11. 8y = 72
  12. 5y = 40

Two-step equations

Class 7 · Worksheet 3 · set 5
Name:Date:Score:    / 12

Solve.

  1. 5m − 19 = 36
  2. 2x + 16 = 32
  3. 4y − 4 = 40
  4. 6x + 12 = 72
  5. 4p + 16 = 40
  6. 8p + 3 = 83
  7. 5y − 17 = 3
  8. 5y + 13 = 38
  9. 8p − 9 = 71
  10. 3y + 4 = 22
  11. 7y + 3 = 38
  12. 2y + 3 = 11

Equations with brackets

Class 7–8 · Worksheet 4 · set 5
Name:Date:Score:    / 10

Solve.

  1. 6(m + 6) = 90
  2. 4(y − 6) + 12 = −8
  3. 3(x + 3) = 27
  4. 3(n + 9) = 57
  5. 5(y + 6) = 60
  6. 5(y + 2) = 35
  7. 4(x − 4) + 13 = 41
  8. 3(n − 4) + 13 = 25
  9. 6(y + 6) = 78
  10. 3(m + 9) = 48

Variables on both sides

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

Solve.

  1. 4m − 2 = 3m + 5
  2. 8y + 13 = 6y + 9
  3. 8x + 12 = 4x + 16
  4. 9n + 15 = 4n + 40
  5. 6y − 10 = y − 45
  6. 6x − 1 = 4x − 9
  7. 9y − 14 = 7y − 2
  8. 5n + 5 = 3n − 3
  9. 6y + 20 = 2y + 28
  10. 5x − 6 = 4x − 8

Equation word problems

Class 7–8 · Worksheet 6 · set 5
Name:Date:Score:    / 6

Form an equation and solve.

  1. The sum of two consecutive numbers is 69. Find the numbers.
  2. The sum of two consecutive numbers is 105. Find the numbers.
  3. I think of a number, multiply it by 4 and add 15. The answer is 31. What is the number?
  4. A father is 4 times as old as his son. The sum of their ages is 75 years. Find their ages.
  5. The length of a rectangle is 3 cm more than its width. Its perimeter is 18 cm. Find the length and the width.
  6. The sum of two consecutive numbers is 27. Find the numbers.

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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.