Question

Solve the given inequality for real x: `1/2 ((3x)/5 + 4) >= 1/3 (x -6)`

Answer 1

The given inequality `1/2 ((3x)/5 + 4) >= 1/3 (x -6)`

= `3((3x + 20)/5) ≥  2(x - 6)`

= `(9x)/5 + 12 ≥ 2x - 12`

= `12 + 12 ≥ 2x - (9x)/5`

= `24 ≥ (10x - 9x)/5`

= `24 ≥ x/5`

= 120 ≥ x

Thus, all real numbers x, which are less than or equal to 120, are the solutions of the given inequality.

Hence, the solution set of the given inequality is (–∞, 120].