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Question
Solve the given inequality for real x: `(3(x-2))/5 <= (5(2-x))/3`
Solution
`(3(x - 2))/5 <= (5(2 - x))/3`
= 9 (x - 2) ≤ 25 (2 - x)
= 9x - 18 ≤ 50 - 25x
= 9x - 18 + 25x ≤ 50
= 34x - 18 ≤ 50
= 34x ≤ 50 + 18
= 34x ≤ 68
= `(34x)/34 ≤ 68/34`
= x ≤ 2
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].
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