Question

Solve the following inequation and represent the solution set on the number line 2x – 5 ≤ 5x + 4 < 11, where x ∈ I.

Answer 1

2x – 5 ≤ 5x + 4 and 5x + 4 < 11

2x – 5x ≤ 4 + 5 and 5x < 11 – 4

3x ≤ – 9 and 5x < 7

`x ≥ 9/(-3) and x < 7/5`

`x ≥ -3 and x < 1 2/5`

`-3 ≤ x ≤ 1 2/5`

Since x ∈ I, the solution set is {–3, –2 –1, 0, 1}.