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].