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