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Question
Solve the given inequality for real x: `x/4 < (5x - 2)/3 - (7x - 3)/5`
Solution
`x/4 < (5x - 2)/3 - (7x - 3)/5`
`x/4 < (5(5x - 2))/3 - (3(7x - 3))/5`
= `x/4 < (25x - 10 - 21x + 9)/15`
= `x/4 < (4x - 1)/15`
= 15x < 4 (4x - 1)
= 15x < 16x - 4
= 4 < 16x - 15x
= 4 < x
Thus, all real numbers x, which are greater than 4, are the solutions of the given inequality.
Hence, the solution set of the given inequality is (4, ∞).
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