# Solve the inequality `x/5 < 3/(6x-1)` .

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### 1 Answer

The inequality to be solved is `x/5 < 3/(6x-1)`

`x/5 < 3/(6x-1)`

=> x(6x - 1) < 15

=> 6x^2 - x < 15

=> 6x^2 - x - 15 < 0

=> 6x^2 + 9x - 10x - 15 < 0

=> 3x(2x + 3) - 5(2x + 3) < 0

=> (3x - 5)(2x + 3) < 0

This is true when either of 3x - 5 or 2x + 3 is negative and the other is positive.

3x - 5 < 0 and 2x + 3 > 0

=> x < 5/3 and x > -3/2

3x - 5 > 0 and 2x + 3 < 0

=> x > 5/3 and x < -3/2

This cannot be true as no value of x is greater than 5/3 and less that -3/2

**The possible values of x at satisfy x/5 < 3/(6x-1) lie in the set {-3/2, 5/3}**