Question

Solve the given inequality for real x: 2(2x + 3) - 10 < 6 (x - 2).

Answer 1

2(2x + 3) - 10 < 6 (x - 2)
⇒ 4x + 6 - 10 < 6x - 12
⇒ 4x - 4 < 6x - 12
⇒ - 4 + 12 < 6x - 4x
⇒ 8 < 2x
⇒ 4 < x
Thus, all real numbers x, which are greater than or equal to 4, are the solutions of the given inequality.
Hence, the solution set of the given inequality is [4, ∞).