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Solve log(2).(x-4)/(2x+5) lt 1....

Solve `log_(2).(x-4)/(2x+5) lt 1`.

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The correct Answer is:
`x in (- infty, - 14/3)cup (4, infty)`
`log_(2).(x-4)/(2x+5) lt 1`
` rArr 0 lt (x-4)/(2x+5) lt 2^(1)`
` rArr (x-4)/(2x+5) gt 0 and (x-4)/(2x+5) lt 2`
` rArr(x-4)/(2x+5) gt 0 and (x-4)/(2x+5) -2 lt 0`
`rArr (x-4)/(2x+5) gt 0and (-3x-14)/(2x+5) lt 0`
`rArr (x-4)/(2x+5) gt 0 and (3x+14)/(2x+5) gt 0`
`rArr x lt - 5//2 or x gt 4 and x lt - 14//3 or x gt - 5//2`
` rArr x in (-infty, -14//3) cup(4, infty)`
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