Question

Solve the given inequality for real x: 3(x – 1) ≤ 2 (x – 3)

Answer 1

3(x – 1) ≤ 2(x – 3)
⇒ 3x – 3 ≤ 2x – 6
⇒ 3x – 3 + 3 ≤ 2x – 6 + 3
⇒ 3x ≤ 2x – 3
⇒ 3x – 2x ≤ 2x – 3 – 2x
⇒ x ≤ – 3

Thus, all real numbers x, which are less than or equal to –3, are the solutions of the given inequality.
Hence, the solution set of the given inequality is (–∞, –3].