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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 72

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 72
Name:Date:Score:    / 12

Solve.

  1. m + 27 = 45
  2. n − 19 = 6
  3. y + 17 = 33
  4. x + 17 = 46
  5. m + 22 = 49
  6. n + 4 = 12
  7. y + 4 = 18
  8. x + 6 = 11
  9. 13 + n = 42
  10. 2 + x = 4
  11. 4 + p = 30
  12. n + 3 = 9

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 72
Name:Date:Score:    / 12

Solve.

  1. 5n = 35
  2. m/3 = 2
  3. y/3 = 2
  4. 6y = 42
  5. p/9 = 1
  6. 4n = 52
  7. 8x = 64
  8. 8m = 24
  9. x/6 = 3
  10. 3p = 27
  11. 2x = 18
  12. 5x = 15

Two-step equations

Class 7 · Worksheet 3 · set 72
Name:Date:Score:    / 12

Solve.

  1. 2n − 12 = 4
  2. 8p + 8 = 96
  3. 4y − 20 = 28
  4. 6y + 9 = 45
  5. 6n − 5 = 37
  6. 4y + 14 = 34
  7. 2x − 3 = 1
  8. 8n + 7 = 39
  9. 7n − 8 = 62
  10. 9n + 8 = 71
  11. 5n − 11 = 39
  12. 7x + 4 = 46

Equations with brackets

Class 7–8 · Worksheet 4 · set 72
Name:Date:Score:    / 10

Solve.

  1. 4(x + 7) = 40
  2. 3(n + 8) = 39
  3. 6(m − 2) + 7 = 25
  4. 2(n − 5) + 11 = 19
  5. 3(y − 3) + 5 = 17
  6. 4(y + 8) = 48
  7. 4(y − 4) + 2 = 2
  8. 2(m − 9) + 12 = 16
  9. 2(n − 7) + 15 = 11
  10. 4(n + 3) = 48

Variables on both sides

Class 8 · Worksheet 5 · set 72
Name:Date:Score:    / 10

Solve.

  1. 8y + 9 = 6y + 1
  2. 6m − 1 = 3m + 20
  3. 8y + 4 = 5y + 10
  4. 8n + 17 = 5n + 41
  5. 3m + 3 = m − 9
  6. 7x − 15 = 2x − 20
  7. 8n − 13 = 4n − 5
  8. 7y + 8 = 3y + 32
  9. 7x − 10 = 2x + 10
  10. 4x − 14 = x + 10

Equation word problems

Class 7–8 · Worksheet 6 · set 72
Name:Date:Score:    / 6

Form an equation and solve.

  1. The length of a rectangle is 7 cm more than its width. Its perimeter is 94 cm. Find the length and the width.
  2. Ravi has ₹28 more than Asha. Together they have ₹424. How much money does Asha have?
  3. Ravi has ₹25 more than Asha. Together they have ₹305. How much money does Asha have?
  4. A father is 5 times as old as his son. The sum of their ages is 90 years. Find their ages.
  5. A father is 4 times as old as his son. The sum of their ages is 65 years. Find their ages.
  6. A father is 5 times as old as his son. The sum of their ages is 48 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.