Question

Given x ∈ {integers}, find the solution set of:

–5 ≤ 2x – 3 < x + 2

Answer 1

–5 ≤ 2x – 3 < x + 2

${\displaystyle \Rightarrow }$ –5 ≤ 2x – 3 and 2x – 3 < x + 2

${\displaystyle \Rightarrow }$ –5 + 3 ≤ 2x and 2x – x < 2 + 3

${\displaystyle \Rightarrow }$ –2 ≤ 2x and x < 5

${\displaystyle \Rightarrow }$ x ≥ –1 and x < 5

Since x ∈ {integers}

‌∴ Solution set = {–1, 0, 1, 2, 3, 4}