Question

Solve the given inequality for real x: 3(2 - x) ≥ 2(1 - x)

Answer 1

3(2–x) ≥ 2(1–x)
⇒ 6–3x ≥ 2–2x
⇒ 6–3x+2x ≥ 2–2x+2x
⇒ 6–x ≥ 2
⇒ 6–x–6 ≥ 2–6
⇒ –x ≥ –4
⇒ x ≤ 4
Thus, all real numbers x, which are less than or equal to 4, are the solutions of the given inequality.

Hence, the solution set of the given inequality is (–∞, 4].