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MathsAges 16-18

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 16-18

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 7x + 15 = 85.

    LHS=RHS
    7 · 15 · 85 · Linear equations

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

    LHS=RHS
    7 · 22 · 57 · Linear equations

  3. 3. Solve 5x + 11 = 76.

    LHS=RHS
    5 · 11 · 76 · Linear equations

  4. 4. Solve 11x + 23 = 89.

    LHS=RHS
    11 · 23 · 89 · Linear equations

  5. 5. Solve 11x + 5 = 203.

    LHS=RHS
    11 · 5 · 203 · Linear equations

  6. 6. Solve 6x + 24 = 84.

    LHS=RHS
    6 · 24 · 84 · Linear equations

  7. 7. Solve 6x + 7 = 115.

    LHS=RHS
    6 · 7 · 115 · Linear equations

  8. 8. Solve 12x + 16 = 196.

    LHS=RHS
    12 · 16 · 196 · Linear equations

  9. 9. Solve 12x + 4 = 100.

    LHS=RHS
    12 · 4 · 100 · Linear equations

  10. 10. Solve 9x + 29 = 110.

    LHS=RHS
    9 · 29 · 110 · Linear equations

  11. 11. Solve 5x + 2 = 92.

    LHS=RHS
    5 · 2 · 92 · Linear equations

  12. 12. Solve 10x + 20 = 200.

    LHS=RHS
    10 · 20 · 200 · Linear equations
12 questions · Seed 56 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 7x + 15 = 85.

    10

    Subtract 15, then divide by 7. x = 10. Check: 7 × 10 + 15 = 85.

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

    5

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

  3. 3. Solve 5x + 11 = 76.

    13

    Subtract 11, then divide by 5. x = 13. Check: 5 × 13 + 11 = 76.

  4. 4. Solve 11x + 23 = 89.

    6

    Subtract 23, then divide by 11. x = 6. Check: 11 × 6 + 23 = 89.

  5. 5. Solve 11x + 5 = 203.

    18

    Subtract 5, then divide by 11. x = 18. Check: 11 × 18 + 5 = 203.

  6. 6. Solve 6x + 24 = 84.

    10

    Subtract 24, then divide by 6. x = 10. Check: 6 × 10 + 24 = 84.

  7. 7. Solve 6x + 7 = 115.

    18

    Subtract 7, then divide by 6. x = 18. Check: 6 × 18 + 7 = 115.

  8. 8. Solve 12x + 16 = 196.

    15

    Subtract 16, then divide by 12. x = 15. Check: 12 × 15 + 16 = 196.

  9. 9. Solve 12x + 4 = 100.

    8

    Subtract 4, then divide by 12. x = 8. Check: 12 × 8 + 4 = 100.

  10. 10. Solve 9x + 29 = 110.

    9

    Subtract 29, then divide by 9. x = 9. Check: 9 × 9 + 29 = 110.

  11. 11. Solve 5x + 2 = 92.

    18

    Subtract 2, then divide by 5. x = 18. Check: 5 × 18 + 2 = 92.

  12. 12. Solve 10x + 20 = 200.

    18

    Subtract 20, then divide by 10. x = 18. Check: 10 × 18 + 20 = 200.

12 questions · Seed 56 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 7x + 15 = 85.

    LHS=RHS
    7 · 15 · 85 · Linear equations

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

    LHS=RHS
    7 · 22 · 57 · Linear equations

  3. 3. Solve 5x + 11 = 76.

    LHS=RHS
    5 · 11 · 76 · Linear equations

  4. 4. Solve 11x + 23 = 89.

    LHS=RHS
    11 · 23 · 89 · Linear equations

  5. 5. Solve 11x + 5 = 203.

    LHS=RHS
    11 · 5 · 203 · Linear equations

  6. 6. Solve 6x + 24 = 84.

    LHS=RHS
    6 · 24 · 84 · Linear equations

  7. 7. Solve 6x + 7 = 115.

    LHS=RHS
    6 · 7 · 115 · Linear equations

  8. 8. Solve 12x + 16 = 196.

    LHS=RHS
    12 · 16 · 196 · Linear equations

  9. 9. Solve 12x + 4 = 100.

    LHS=RHS
    12 · 4 · 100 · Linear equations

  10. 10. Solve 9x + 29 = 110.

    LHS=RHS
    9 · 29 · 110 · Linear equations

  11. 11. Solve 5x + 2 = 92.

    LHS=RHS
    5 · 2 · 92 · Linear equations

  12. 12. Solve 10x + 20 = 200.

    LHS=RHS
    10 · 20 · 200 · Linear equations
12 questions · Seed 56 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 7x + 15 = 85.

    10

    Subtract 15, then divide by 7. x = 10. Check: 7 × 10 + 15 = 85.

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

    5

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

  3. 3. Solve 5x + 11 = 76.

    13

    Subtract 11, then divide by 5. x = 13. Check: 5 × 13 + 11 = 76.

  4. 4. Solve 11x + 23 = 89.

    6

    Subtract 23, then divide by 11. x = 6. Check: 11 × 6 + 23 = 89.

  5. 5. Solve 11x + 5 = 203.

    18

    Subtract 5, then divide by 11. x = 18. Check: 11 × 18 + 5 = 203.

  6. 6. Solve 6x + 24 = 84.

    10

    Subtract 24, then divide by 6. x = 10. Check: 6 × 10 + 24 = 84.

  7. 7. Solve 6x + 7 = 115.

    18

    Subtract 7, then divide by 6. x = 18. Check: 6 × 18 + 7 = 115.

  8. 8. Solve 12x + 16 = 196.

    15

    Subtract 16, then divide by 12. x = 15. Check: 12 × 15 + 16 = 196.

  9. 9. Solve 12x + 4 = 100.

    8

    Subtract 4, then divide by 12. x = 8. Check: 12 × 8 + 4 = 100.

  10. 10. Solve 9x + 29 = 110.

    9

    Subtract 29, then divide by 9. x = 9. Check: 9 × 9 + 29 = 110.

  11. 11. Solve 5x + 2 = 92.

    18

    Subtract 2, then divide by 5. x = 18. Check: 5 × 18 + 2 = 92.

  12. 12. Solve 10x + 20 = 200.

    18

    Subtract 20, then divide by 10. x = 18. Check: 10 × 18 + 20 = 200.

12 questions · Seed 56 · Age guidance, not curriculum certification