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Question
Solve the given inequality for real x: `((2x- 1))/3 >= ((3x - 2))/4 - ((2 - x))/5`
Solution
The given inequality,
`((2x- 1))/3 >= ((3x - 2))/4 - ((2 - x))/5`
= `((2x- 1))/3 >= (5(3x - 2) -4 (2 - x))/20`
= `(2x - 1)/3 >= (15x - 10 - 8 + 4x)/20`
= `(2x - 1)/3 >= (19x - 18)/20`
= 20 (2x - 1) ≥ 3 (19x - 18)
= 40x - 20 ≥ 57x - 54
= -20 + 54 ≥ 57x - 40x
= 34 ≥ 17x
= 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].
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