1.

`if (5x)/(4) + (3x)/(8) gt (39)/(8) " and " (2x-1)/(12)-(x-1)/(3)lt(3x+1)/(4)`, then x belongs to the internalA. `(3, oo)`B. `(0, oo)`C. `(-oo, 3)`D. `(-oo, 0)`

Answer» Correct Answer - A
We have,
`(5x)/(4) + (3x)/(8) gt (39)/(8) " and " (2x-1)/(12)-(x-1)/(3)lt(3x+1)/(4)`
`rArr (10x+3x)/(8) gt (39)/(8) " and " (2x-1-4x+4)/(12) lt (3x + 1)/(4)`
`rArr (13x)/(8) gt (39)/(8) " and " (-2x+3)/(12) lt (3x+1)/(4)`
`rArr 13x gt 39 " and " -2x + 3 lt 9x + 3`
`rArr x gt 3 " and " -11x lt 0`
`rArr x gt 3 " and " x gt 0`
`rArr x in (3, oo) " and " x in (0, oo) rArr x in (3, oo)`


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