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MathsAges 13-15

Linear equations

Solve a linear equation by reversing addition and multiplication, then substitute your answer to check it. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 9x + 21 = 57.

    LHS=RHS
    9 · 21 · 57 · Linear equations

  2. 2. Solve 2x + 3 = 35.

    LHS=RHS
    2 · 3 · 35 · Linear equations

  3. 3. Solve 3x + 29 = 47.

    LHS=RHS
    3 · 29 · 47 · Linear equations

  4. 4. Solve 2x + 21 = 51.

    LHS=RHS
    2 · 21 · 51 · Linear equations

  5. 5. Solve 2x + 3 = 29.

    LHS=RHS
    2 · 3 · 29 · Linear equations

  6. 6. Solve 9x + 22 = 157.

    LHS=RHS
    9 · 22 · 157 · Linear equations

  7. 7. Solve 2x + 26 = 62.

    LHS=RHS
    2 · 26 · 62 · Linear equations

  8. 8. Solve 12x + 16 = 28.

    LHS=RHS
    12 · 16 · 28 · Linear equations

  9. 9. Solve 2x + 30 = 64.

    LHS=RHS
    2 · 30 · 64 · Linear equations

  10. 10. Solve 7x + 22 = 57.

    LHS=RHS
    7 · 22 · 57 · Linear equations

  11. 11. Solve 3x + 4 = 40.

    LHS=RHS
    3 · 4 · 40 · Linear equations

  12. 12. Solve 12x + 22 = 142.

    LHS=RHS
    12 · 22 · 142 · Linear equations
12 questions · Seed 45 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 9x + 21 = 57.

    4

    Subtract 21, then divide by 9. x = 4. Check: 9 × 4 + 21 = 57.

  2. 2. Solve 2x + 3 = 35.

    16

    Subtract 3, then divide by 2. x = 16. Check: 2 × 16 + 3 = 35.

  3. 3. Solve 3x + 29 = 47.

    6

    Subtract 29, then divide by 3. x = 6. Check: 3 × 6 + 29 = 47.

  4. 4. Solve 2x + 21 = 51.

    15

    Subtract 21, then divide by 2. x = 15. Check: 2 × 15 + 21 = 51.

  5. 5. Solve 2x + 3 = 29.

    13

    Subtract 3, then divide by 2. x = 13. Check: 2 × 13 + 3 = 29.

  6. 6. Solve 9x + 22 = 157.

    15

    Subtract 22, then divide by 9. x = 15. Check: 9 × 15 + 22 = 157.

  7. 7. Solve 2x + 26 = 62.

    18

    Subtract 26, then divide by 2. x = 18. Check: 2 × 18 + 26 = 62.

  8. 8. Solve 12x + 16 = 28.

    1

    Subtract 16, then divide by 12. x = 1. Check: 12 × 1 + 16 = 28.

  9. 9. Solve 2x + 30 = 64.

    17

    Subtract 30, then divide by 2. x = 17. Check: 2 × 17 + 30 = 64.

  10. 10. Solve 7x + 22 = 57.

    5

    Subtract 22, then divide by 7. x = 5. Check: 7 × 5 + 22 = 57.

  11. 11. Solve 3x + 4 = 40.

    12

    Subtract 4, then divide by 3. x = 12. Check: 3 × 12 + 4 = 40.

  12. 12. Solve 12x + 22 = 142.

    10

    Subtract 22, then divide by 12. x = 10. Check: 12 × 10 + 22 = 142.

12 questions · Seed 45 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 9x + 21 = 57.

    LHS=RHS
    9 · 21 · 57 · Linear equations

  2. 2. Solve 2x + 3 = 35.

    LHS=RHS
    2 · 3 · 35 · Linear equations

  3. 3. Solve 3x + 29 = 47.

    LHS=RHS
    3 · 29 · 47 · Linear equations

  4. 4. Solve 2x + 21 = 51.

    LHS=RHS
    2 · 21 · 51 · Linear equations

  5. 5. Solve 2x + 3 = 29.

    LHS=RHS
    2 · 3 · 29 · Linear equations

  6. 6. Solve 9x + 22 = 157.

    LHS=RHS
    9 · 22 · 157 · Linear equations

  7. 7. Solve 2x + 26 = 62.

    LHS=RHS
    2 · 26 · 62 · Linear equations

  8. 8. Solve 12x + 16 = 28.

    LHS=RHS
    12 · 16 · 28 · Linear equations

  9. 9. Solve 2x + 30 = 64.

    LHS=RHS
    2 · 30 · 64 · Linear equations

  10. 10. Solve 7x + 22 = 57.

    LHS=RHS
    7 · 22 · 57 · Linear equations

  11. 11. Solve 3x + 4 = 40.

    LHS=RHS
    3 · 4 · 40 · Linear equations

  12. 12. Solve 12x + 22 = 142.

    LHS=RHS
    12 · 22 · 142 · Linear equations
12 questions · Seed 45 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 9x + 21 = 57.

    4

    Subtract 21, then divide by 9. x = 4. Check: 9 × 4 + 21 = 57.

  2. 2. Solve 2x + 3 = 35.

    16

    Subtract 3, then divide by 2. x = 16. Check: 2 × 16 + 3 = 35.

  3. 3. Solve 3x + 29 = 47.

    6

    Subtract 29, then divide by 3. x = 6. Check: 3 × 6 + 29 = 47.

  4. 4. Solve 2x + 21 = 51.

    15

    Subtract 21, then divide by 2. x = 15. Check: 2 × 15 + 21 = 51.

  5. 5. Solve 2x + 3 = 29.

    13

    Subtract 3, then divide by 2. x = 13. Check: 2 × 13 + 3 = 29.

  6. 6. Solve 9x + 22 = 157.

    15

    Subtract 22, then divide by 9. x = 15. Check: 9 × 15 + 22 = 157.

  7. 7. Solve 2x + 26 = 62.

    18

    Subtract 26, then divide by 2. x = 18. Check: 2 × 18 + 26 = 62.

  8. 8. Solve 12x + 16 = 28.

    1

    Subtract 16, then divide by 12. x = 1. Check: 12 × 1 + 16 = 28.

  9. 9. Solve 2x + 30 = 64.

    17

    Subtract 30, then divide by 2. x = 17. Check: 2 × 17 + 30 = 64.

  10. 10. Solve 7x + 22 = 57.

    5

    Subtract 22, then divide by 7. x = 5. Check: 7 × 5 + 22 = 57.

  11. 11. Solve 3x + 4 = 40.

    12

    Subtract 4, then divide by 3. x = 12. Check: 3 × 12 + 4 = 40.

  12. 12. Solve 12x + 22 = 142.

    10

    Subtract 22, then divide by 12. x = 10. Check: 12 × 10 + 22 = 142.

12 questions · Seed 45 · Age guidance, not curriculum certification