Question

Solve the following inequalities in the given universal set:
2x - 5 ≤ 5x + 4 < 11, where x ∈ I.

Answer 1

2x - 5 ≤ 5x + 4 < 11, x ∈ I.
2x - 5 ≤ 5x + 4
2x - 5x ≤ 4 + 5
-3x ≤ 9
3x ≥ -3
or
-3 ≤ x
5x + 4 < 11
5x < 11 - 4
5x < 7
x < `(7)/(5)`

x < 1`(2)/(5)`
From (1) and (2) `-3 ≤ x < 1(2)/(5), x ∈ "I"`
∴ Solution set = {-3, -2, -1, 0, 1}