InterviewSolution
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InterviewSolution
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Solve: `|(2x-1)/(x-1)|gt2,x in R` |
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Answer» Correct Answer - `((3)/(4),1)uu(1,oo)` Using`|x|gta iff x lt -a x gt a`, we have `|(2x-1)/(x-1)|gt2 iff(2x-1)/(x-1)lt-2or(2x-1)/(x-1)gt2`. Case I When`(2x-1)/(x-1)lt-2` `(2x-1)/(x-1)+2lt0 rArr (2x-1+2x-2)/(x-1) lt 0 rArr (4x-3)/(x-1) lt 0`. `therefore (4x-3 lt0and x-1gt0)or(4x-3 gt0 and x-1lt0)` `rArr (xlt(3)/(4)andxgt1) or(xgt(3)/(4) and x lt1)` `rArr (3)/(4)ltxlt1 rArr x in((3)/(4),1)`. Case II When `(2x-1)/(x-1) gt 2` Then, `(2x-1)/(x-1) -2 gt 0 rArr (2x-1-2x+2)/(x-1) gt 0 rArr (1)/(x-1) gt0` `rArr x-1gt0rArr gt1 rArrx in(1,oo)`. `therefore "solution set " =((3)/(4),1)uu(1,oo)`. |
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