Question

Solve the given inequality for real x: 37 ­– (3x + 5) ≥ 9x – 8(x – 3)

Answer 1

The given inequality,
37 – (3x + 5) ≥ 9x – 8(x – 3)

37 – 3x - 5 ≥ 9x – 8x + 24

– 3x + 32 ≥ x + 24

32 - 24 ≥ x + 3x

8 ≥ 4x

= 2 ≥ x

Thus, all real numbers x, which are less than or equal to 2, are the solutions of the given inequality.

Hence, the solution set of the given inequality is (–∞, 2].