Solve the inequality

6 ≤ –3 (2x – 4) < 12

Given inequality

⇒ 6 ≤ -3 (2x – 4) < 12

Dividing the inequality by 3 we get.

⇒ 2 ≤ - (2x – 4) < 4

Multiplying the inequality by -1.

⇒ -2 ≥ 2x – 4 > -4 [multiplying the inequality with -1 changes the inequality sign.]

⇒ -2 + 4 ≥ 2x – 4 + 4 > -4 + 4

⇒ 2 ≥ 2x > 0

Dividing the inequality by 2

⇒ 0 < x ≤ 1

∴ all real numbers x greater than 0 but less than or equal to 1 are solution of given equality.

x ∈ (0, 1]