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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 6x + 7 = 103.

    LHS=RHS
    6 · 7 · 103 · Linear equations

  2. 2. Solve 3x + 20 = 23.

    LHS=RHS
    3 · 20 · 23 · Linear equations

  3. 3. Solve 9x + 15 = 186.

    LHS=RHS
    9 · 15 · 186 · Linear equations

  4. 4. Solve 7x + 16 = 23.

    LHS=RHS
    7 · 16 · 23 · Linear equations

  5. 5. Solve 4x + 11 = 75.

    LHS=RHS
    4 · 11 · 75 · Linear equations

  6. 6. Solve 7x + 10 = 101.

    LHS=RHS
    7 · 10 · 101 · Linear equations

  7. 7. Solve 3x + 16 = 22.

    LHS=RHS
    3 · 16 · 22 · Linear equations

  8. 8. Solve 3x + 29 = 41.

    LHS=RHS
    3 · 29 · 41 · Linear equations

  9. 9. Solve 6x + 24 = 54.

    LHS=RHS
    6 · 24 · 54 · Linear equations

  10. 10. Solve 11x + 28 = 138.

    LHS=RHS
    11 · 28 · 138 · Linear equations

  11. 11. Solve 5x + 7 = 17.

    LHS=RHS
    5 · 7 · 17 · Linear equations

  12. 12. Solve 6x + 11 = 107.

    LHS=RHS
    6 · 11 · 107 · Linear equations
12 questions · Seed 48 · 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 6x + 7 = 103.

    16

    Subtract 7, then divide by 6. x = 16. Check: 6 × 16 + 7 = 103.

  2. 2. Solve 3x + 20 = 23.

    1

    Subtract 20, then divide by 3. x = 1. Check: 3 × 1 + 20 = 23.

  3. 3. Solve 9x + 15 = 186.

    19

    Subtract 15, then divide by 9. x = 19. Check: 9 × 19 + 15 = 186.

  4. 4. Solve 7x + 16 = 23.

    1

    Subtract 16, then divide by 7. x = 1. Check: 7 × 1 + 16 = 23.

  5. 5. Solve 4x + 11 = 75.

    16

    Subtract 11, then divide by 4. x = 16. Check: 4 × 16 + 11 = 75.

  6. 6. Solve 7x + 10 = 101.

    13

    Subtract 10, then divide by 7. x = 13. Check: 7 × 13 + 10 = 101.

  7. 7. Solve 3x + 16 = 22.

    2

    Subtract 16, then divide by 3. x = 2. Check: 3 × 2 + 16 = 22.

  8. 8. Solve 3x + 29 = 41.

    4

    Subtract 29, then divide by 3. x = 4. Check: 3 × 4 + 29 = 41.

  9. 9. Solve 6x + 24 = 54.

    5

    Subtract 24, then divide by 6. x = 5. Check: 6 × 5 + 24 = 54.

  10. 10. Solve 11x + 28 = 138.

    10

    Subtract 28, then divide by 11. x = 10. Check: 11 × 10 + 28 = 138.

  11. 11. Solve 5x + 7 = 17.

    2

    Subtract 7, then divide by 5. x = 2. Check: 5 × 2 + 7 = 17.

  12. 12. Solve 6x + 11 = 107.

    16

    Subtract 11, then divide by 6. x = 16. Check: 6 × 16 + 11 = 107.

12 questions · Seed 48 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Linear equations

Take your time. Show your thinking.

  1. 1. Solve 6x + 7 = 103.

    LHS=RHS
    6 · 7 · 103 · Linear equations

  2. 2. Solve 3x + 20 = 23.

    LHS=RHS
    3 · 20 · 23 · Linear equations

  3. 3. Solve 9x + 15 = 186.

    LHS=RHS
    9 · 15 · 186 · Linear equations

  4. 4. Solve 7x + 16 = 23.

    LHS=RHS
    7 · 16 · 23 · Linear equations

  5. 5. Solve 4x + 11 = 75.

    LHS=RHS
    4 · 11 · 75 · Linear equations

  6. 6. Solve 7x + 10 = 101.

    LHS=RHS
    7 · 10 · 101 · Linear equations

  7. 7. Solve 3x + 16 = 22.

    LHS=RHS
    3 · 16 · 22 · Linear equations

  8. 8. Solve 3x + 29 = 41.

    LHS=RHS
    3 · 29 · 41 · Linear equations

  9. 9. Solve 6x + 24 = 54.

    LHS=RHS
    6 · 24 · 54 · Linear equations

  10. 10. Solve 11x + 28 = 138.

    LHS=RHS
    11 · 28 · 138 · Linear equations

  11. 11. Solve 5x + 7 = 17.

    LHS=RHS
    5 · 7 · 17 · Linear equations

  12. 12. Solve 6x + 11 = 107.

    LHS=RHS
    6 · 11 · 107 · Linear equations
12 questions · Seed 48 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Linear equations

Answers and reasoning. Review before teaching.

  1. 1. Solve 6x + 7 = 103.

    16

    Subtract 7, then divide by 6. x = 16. Check: 6 × 16 + 7 = 103.

  2. 2. Solve 3x + 20 = 23.

    1

    Subtract 20, then divide by 3. x = 1. Check: 3 × 1 + 20 = 23.

  3. 3. Solve 9x + 15 = 186.

    19

    Subtract 15, then divide by 9. x = 19. Check: 9 × 19 + 15 = 186.

  4. 4. Solve 7x + 16 = 23.

    1

    Subtract 16, then divide by 7. x = 1. Check: 7 × 1 + 16 = 23.

  5. 5. Solve 4x + 11 = 75.

    16

    Subtract 11, then divide by 4. x = 16. Check: 4 × 16 + 11 = 75.

  6. 6. Solve 7x + 10 = 101.

    13

    Subtract 10, then divide by 7. x = 13. Check: 7 × 13 + 10 = 101.

  7. 7. Solve 3x + 16 = 22.

    2

    Subtract 16, then divide by 3. x = 2. Check: 3 × 2 + 16 = 22.

  8. 8. Solve 3x + 29 = 41.

    4

    Subtract 29, then divide by 3. x = 4. Check: 3 × 4 + 29 = 41.

  9. 9. Solve 6x + 24 = 54.

    5

    Subtract 24, then divide by 6. x = 5. Check: 6 × 5 + 24 = 54.

  10. 10. Solve 11x + 28 = 138.

    10

    Subtract 28, then divide by 11. x = 10. Check: 11 × 10 + 28 = 138.

  11. 11. Solve 5x + 7 = 17.

    2

    Subtract 7, then divide by 5. x = 2. Check: 5 × 2 + 7 = 17.

  12. 12. Solve 6x + 11 = 107.

    16

    Subtract 11, then divide by 6. x = 16. Check: 6 × 16 + 11 = 107.

12 questions · Seed 48 · Age guidance, not curriculum certification