Question
Mathematics Question on inequalities
Solve the given inequality for real x: 37 – (3x + 5) ≥ 9x – 8(x – 3)
Answer
37 - (3x + 5) ≥ 9x - 8(x - 3)
⇒ 37 - 3x - 5 ≥ 9x - 8x + 24
⇒ 32 - 3x ≥ 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].