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Free · Class 6–8 · 6 worksheets · answer keys · practise online · set 23

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 23
Name:Date:Score:    / 12

Solve.

  1. x + 5 = 27
  2. m + 7 = 9
  3. 18 + p = 37
  4. 28 + m = 29
  5. y − 10 = 19
  6. p + 8 = 14
  7. y − 26 = 3
  8. m − 19 = 5
  9. 25 + y = 49
  10. y − 20 = 1
  11. n + 13 = 18
  12. x − 11 = 9

One-step equations (× and ÷)

Class 6–7 · Worksheet 2 · set 23
Name:Date:Score:    / 12

Solve.

  1. n/5 = 11
  2. 4y = 4
  3. 5n = 45
  4. 7m = 105
  5. x/9 = 2
  6. 5m = 55
  7. m/9 = 3
  8. n/3 = 14
  9. y/6 = 12
  10. 3m = 12
  11. x/8 = 14
  12. 2n = 14

Two-step equations

Class 7 · Worksheet 3 · set 23
Name:Date:Score:    / 12

Solve.

  1. 5y − 3 = 7
  2. 9x − 17 = 19
  3. 9m + 13 = 67
  4. 3p + 11 = 29
  5. 6m + 15 = 51
  6. 7p + 7 = 63
  7. 2n + 9 = 17
  8. 7m + 20 = 48
  9. 5p + 9 = 24
  10. 5x + 15 = 50
  11. 8p − 15 = 65
  12. 5n + 5 = 25

Equations with brackets

Class 7–8 · Worksheet 4 · set 23
Name:Date:Score:    / 10

Solve.

  1. 5(x + 7) = 80
  2. 2(y − 3) + 15 = 29
  3. 3(y + 3) = 39
  4. 5(y − 8) + 4 = 9
  5. 5(m − 1) + 8 = 18
  6. 2(y − 1) + 3 = 11
  7. 2(n + 3) = 24
  8. 6(n + 6) = 60
  9. 6(m − 3) + 14 = 26
  10. 3(y − 6) + 6 = 24

Variables on both sides

Class 8 · Worksheet 5 · set 23
Name:Date:Score:    / 10

Solve.

  1. 3n + 14 = n + 28
  2. 9n + 16 = 2n − 12
  3. 3n − 19 = n − 3
  4. 8x − 13 = 3x + 17
  5. 3y − 7 = y + 3
  6. 5m − 14 = 2m − 32
  7. 4x + 19 = 3x + 28
  8. 5x − 1 = 2x − 7
  9. 8y + 16 = 4y + 44
  10. 7n − 14 = 2n + 16

Equation word problems

Class 7–8 · Worksheet 6 · set 23
Name:Date:Score:    / 6

Form an equation and solve.

  1. The length of a rectangle is 2 cm more than its width. Its perimeter is 44 cm. Find the length and the width.
  2. Ravi has ₹27 more than Asha. Together they have ₹341. How much money does Asha have?
  3. Ravi has ₹44 more than Asha. Together they have ₹312. How much money does Asha have?
  4. I think of a number, multiply it by 6 and add 18. The answer is 102. What is the number?
  5. A father is 4 times as old as his son. The sum of their ages is 65 years. Find their ages.
  6. The length of a rectangle is 2 cm more than its width. Its perimeter is 32 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?

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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.