Question

Find the solution set of –3 < x – 2 ≤ 9 – 2x ; x ∈ Z (set of integers).

Answer 1

– 3 < x – 2 < 9 – 2x 

⇒ – 3 < x – 2 and x – 2 < 9 – 2x ⇒ – 3 + 2 < x and x + 2x < 9 + 2 

⇒ – 1 < x and 3x < 11 or x < \(\frac{11}{3}\) ⇒ − 1 < \(x\) ≤ \(\frac{11}{3}\)

Since \(x\) ∈ Z, so the solution set = {0, 1, 2, 3}.