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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 5x + 29 = 59.

    LHS=RHS
    5 · 29 · 59 · Linear equations

  2. 2. Solve 2x + 9 = 41.

    LHS=RHS
    2 · 9 · 41 · Linear equations

  3. 3. Solve 11x + 29 = 117.

    LHS=RHS
    11 · 29 · 117 · Linear equations

  4. 4. Solve 3x + 18 = 60.

    LHS=RHS
    3 · 18 · 60 · Linear equations

  5. 5. Solve 9x + 15 = 78.

    LHS=RHS
    9 · 15 · 78 · Linear equations

  6. 6. Solve 5x + 4 = 39.

    LHS=RHS
    5 · 4 · 39 · Linear equations

  7. 7. Solve 2x + 30 = 60.

    LHS=RHS
    2 · 30 · 60 · Linear equations

  8. 8. Solve 9x + 9 = 126.

    LHS=RHS
    9 · 9 · 126 · Linear equations

  9. 9. Solve 12x + 13 = 85.

    LHS=RHS
    12 · 13 · 85 · Linear equations

  10. 10. Solve 7x + 29 = 43.

    LHS=RHS
    7 · 29 · 43 · Linear equations

  11. 11. Solve 6x + 12 = 108.

    LHS=RHS
    6 · 12 · 108 · Linear equations

  12. 12. Solve 12x + 14 = 170.

    LHS=RHS
    12 · 14 · 170 · Linear equations
12 questions · Seed 104734 · 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 5x + 29 = 59.

    6

    Subtract 29, then divide by 5. x = 6. Check: 5 × 6 + 29 = 59.

  2. 2. Solve 2x + 9 = 41.

    16

    Subtract 9, then divide by 2. x = 16. Check: 2 × 16 + 9 = 41.

  3. 3. Solve 11x + 29 = 117.

    8

    Subtract 29, then divide by 11. x = 8. Check: 11 × 8 + 29 = 117.

  4. 4. Solve 3x + 18 = 60.

    14

    Subtract 18, then divide by 3. x = 14. Check: 3 × 14 + 18 = 60.

  5. 5. Solve 9x + 15 = 78.

    7

    Subtract 15, then divide by 9. x = 7. Check: 9 × 7 + 15 = 78.

  6. 6. Solve 5x + 4 = 39.

    7

    Subtract 4, then divide by 5. x = 7. Check: 5 × 7 + 4 = 39.

  7. 7. Solve 2x + 30 = 60.

    15

    Subtract 30, then divide by 2. x = 15. Check: 2 × 15 + 30 = 60.

  8. 8. Solve 9x + 9 = 126.

    13

    Subtract 9, then divide by 9. x = 13. Check: 9 × 13 + 9 = 126.

  9. 9. Solve 12x + 13 = 85.

    6

    Subtract 13, then divide by 12. x = 6. Check: 12 × 6 + 13 = 85.

  10. 10. Solve 7x + 29 = 43.

    2

    Subtract 29, then divide by 7. x = 2. Check: 7 × 2 + 29 = 43.

  11. 11. Solve 6x + 12 = 108.

    16

    Subtract 12, then divide by 6. x = 16. Check: 6 × 16 + 12 = 108.

  12. 12. Solve 12x + 14 = 170.

    13

    Subtract 14, then divide by 12. x = 13. Check: 12 × 13 + 14 = 170.

12 questions · Seed 104734 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 5x + 29 = 59.

    LHS=RHS
    5 · 29 · 59 · Linear equations

  2. 2. Solve 2x + 9 = 41.

    LHS=RHS
    2 · 9 · 41 · Linear equations

  3. 3. Solve 11x + 29 = 117.

    LHS=RHS
    11 · 29 · 117 · Linear equations

  4. 4. Solve 3x + 18 = 60.

    LHS=RHS
    3 · 18 · 60 · Linear equations

  5. 5. Solve 9x + 15 = 78.

    LHS=RHS
    9 · 15 · 78 · Linear equations

  6. 6. Solve 5x + 4 = 39.

    LHS=RHS
    5 · 4 · 39 · Linear equations

  7. 7. Solve 2x + 30 = 60.

    LHS=RHS
    2 · 30 · 60 · Linear equations

  8. 8. Solve 9x + 9 = 126.

    LHS=RHS
    9 · 9 · 126 · Linear equations

  9. 9. Solve 12x + 13 = 85.

    LHS=RHS
    12 · 13 · 85 · Linear equations

  10. 10. Solve 7x + 29 = 43.

    LHS=RHS
    7 · 29 · 43 · Linear equations

  11. 11. Solve 6x + 12 = 108.

    LHS=RHS
    6 · 12 · 108 · Linear equations

  12. 12. Solve 12x + 14 = 170.

    LHS=RHS
    12 · 14 · 170 · Linear equations
12 questions · Seed 104734 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 5x + 29 = 59.

    6

    Subtract 29, then divide by 5. x = 6. Check: 5 × 6 + 29 = 59.

  2. 2. Solve 2x + 9 = 41.

    16

    Subtract 9, then divide by 2. x = 16. Check: 2 × 16 + 9 = 41.

  3. 3. Solve 11x + 29 = 117.

    8

    Subtract 29, then divide by 11. x = 8. Check: 11 × 8 + 29 = 117.

  4. 4. Solve 3x + 18 = 60.

    14

    Subtract 18, then divide by 3. x = 14. Check: 3 × 14 + 18 = 60.

  5. 5. Solve 9x + 15 = 78.

    7

    Subtract 15, then divide by 9. x = 7. Check: 9 × 7 + 15 = 78.

  6. 6. Solve 5x + 4 = 39.

    7

    Subtract 4, then divide by 5. x = 7. Check: 5 × 7 + 4 = 39.

  7. 7. Solve 2x + 30 = 60.

    15

    Subtract 30, then divide by 2. x = 15. Check: 2 × 15 + 30 = 60.

  8. 8. Solve 9x + 9 = 126.

    13

    Subtract 9, then divide by 9. x = 13. Check: 9 × 13 + 9 = 126.

  9. 9. Solve 12x + 13 = 85.

    6

    Subtract 13, then divide by 12. x = 6. Check: 12 × 6 + 13 = 85.

  10. 10. Solve 7x + 29 = 43.

    2

    Subtract 29, then divide by 7. x = 2. Check: 7 × 2 + 29 = 43.

  11. 11. Solve 6x + 12 = 108.

    16

    Subtract 12, then divide by 6. x = 16. Check: 6 × 16 + 12 = 108.

  12. 12. Solve 12x + 14 = 170.

    13

    Subtract 14, then divide by 12. x = 13. Check: 12 × 13 + 14 = 170.

12 questions · Seed 104734 · Age guidance, not curriculum certification