Solving inequalities: negatives and brackets

The Maths Habit Handout to print

  1. Solve 3x + 5 < 17

    x < 4

  2. Solve 6x − 1 ≥ 4x + 9

    x ≥ 5

  3. Expand 3(x − 4)

    3x − 12

5 > 2. Kai says that means −5 > −2.
Is Kai right?

No. −5 is to the left of −2 on a number line, so −5 < −2

3 < 7. Multiply both sides by −1. Where are −3 and −7 on the number line?

−3 is to the right of −7, so −3 > −7.

Multiplying or dividing both sides by a negative number turns the sign round.

Does the sign turn round? Decide. Do not solve.

  1. x − 6 < 10

    No: you add 6.

  2. −3x < 15

    Yes: you divide by −3.

  3. 3x < −15

    No: you divide by 3. The −15 does not matter.

  4. 14 − 2x > 4

    Yes: the x term is −2x.

  5. 2x − 14 > 4

    No: the x term is 2x.

6 − 4x < 26

−4x < 20
Answerx > −5
x = 0: 6 − 4 × 0 = 6, and 6 < 26 is true

13 − 2x ≥ 5

−2x ≥ −8
Answerx ≤ 4
x = 0: 13 − 2 × 0 = 13, and 13 ≥ 5 is true

6 − 4x < 26

−4x < 20
Answerx > −5
x = 0: 6 − 4 × 0 = 6, and 6 < 26 is true

2 − 5x ≤ 22

−5x ≤ 20
Answerx ≥ −4
x = 0: 2 − 5 × 0 = 2, and 2 ≤ 22 is true

6 − 4x < 26

−4x < 20
Answerx > −5
x = 0: 6 − 4 × 0 = 6, and 6 < 26 is true

−3x + 7 > 1

−3x > −6
Answerx < 2
x = 0: −3 × 0 + 7 = 7, and 7 > 1 is true

3(x + 4) > 6

3x + 12 > 63x > −6
Answerx > −2
x = 0: 3 × (0 + 4) = 12, and 12 > 6 is true

2(5x − 3) ≥ 19

10x − 6 ≥ 1910x ≥ 25
Answerx ≥ 2.5
x = 3: 2 × (5 × 3 − 3) = 24, and 24 ≥ 19 is true

3(x + 4) > 6

3x + 12 > 63x > −6
Answerx > −2
x = 0: 3 × (0 + 4) = 12, and 12 > 6 is true

5(x − 2) < 15

5x − 10 < 155x < 25
Answerx < 5
x = 0: 5 × (0 − 2) = −10, and −10 < 15 is true

Solve 8 − 3x > 26.

Ax < −6
Bx > −6
Cx > 6
Dx = −6
A: rightB: dividing by −3 turns the sign round: try x = 0, 8 > 26 is falseC: the x term is −3x, not 3xD: the answer is an inequality, never x = …

Solving inequalities: negatives and brackets worksheet, page 1

Solving inequalities: negatives and brackets worksheet, page 2

Answer sheet

  1. Solve 3(4 − x) ≥ 18

    x ≤ −2

  2. Zara has £20. She buys p pens at £3 each and has more than £5 left. Write and solve an inequality for p.

    p < 5

  1. Solve 11 − 4x ≤ 3

    x ≥ 2

  2. Solve 2(x + 5) ≤ 16

    x ≤ 3

  3. Sam solves 20 − 3x < 5 and gets x < 5. Find the right answer.

    x > 5
Exit tickets to print