Solving inequalities

The Maths Habit Handout to print

  1. Write as an inequality: x is greater than 7

    x > 7

  2. Write as an inequality: x is greater than or equal to −3

    x ≥ −3

  3. Which of these numbers fit x < 5?  2,  5,  7,  −1

    2 and −1

  4. Draw x ≤ 4 on a number line.

    A filled circle at 4, arrow to the left

A ride says “Over 1.2 m only”.
Lily is exactly 1.2 m. Can she ride?

No. 1.2 m is not over 1.2 m

Inequality
Shows that one amount is bigger or smaller than another.

<less than >greater than ≤less than or equal to ≥greater than or equal to

Solve

  1. 4x < 20

    x < 5

  2. x + 6 ≥ 2

    x ≥ −4

  3. x − 3 > 1

    x > 4

  4. 5x ≤ 15

    x ≤ 3

3x + 4 < 19

5x − 3 ≥ 12

4x + 7 > 15

− 7 both sides4x > 8
÷ 4 both sidesx > 2
Answerx > 2

2x − 5 ≤ 3

+ 5 both sides2x ≤ 8
÷ 2 both sidesx ≤ 4
Answerx ≤ 4

4x + 7 > 15

− 7 both sides4x > 8
÷ 4 both sidesx > 2
Answerx > 2

3x + 8 ≥ 2

− 8 both sides3x ≥ −6
÷ 3 both sidesx ≥ −2
Answerx ≥ −2

Solving inequalities worksheet, page 1

Solving inequalities worksheet, page 2

Answer sheet

  1. List all the whole numbers that fit −2 < x ≤ 3.

    −1, 0, 1, 2, 3

  2. A taxi costs £3 plus £2 for every mile. Sam has £15. Write and solve an inequality for the number of miles, m, he can travel.

    m ≤ 6

  1. Which of 3, −4, 0 and 5 satisfy x < 3?

    −4 and 0

  2. Solve 3x + 14 ≥ 2

    x ≥ −4

  3. Jess solves 2x + 9 < 21 and gets x < 15. Find the right answer.

    x < 6
Exit tickets to print