Question

Solve the following inequalities

−13 ≤ 5x + 2 ≤ 32, x is an integer

Answer 1

−13 ≤ 5x + 2 ≤ 32

Subtracting throughout by 2

−13 – 2 ≤ 5x + 2 – 2 ≤ 32 – 2

−15 ≤ 5x ≤ 30

Dividing throughout by 5

`(-15)/5` ≤ `(5x)/5` ≤ `30/5`

– 3 ≤ x ≤ 6

∴ Since the solution is an integer between −3 and 6 both inclusive, we have the solution as −3, −2, −1, 0, 1, 2, 3, 4, 5, 6.

∴ x = −3, −2, −1, 0, 1, 2, 3, 4, 5 and 6.