InterviewSolution
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InterviewSolution
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For `2 lt x lt 4` find the values of |x|. (ii) For `-3 le x le -1`, find the values of |x|. (iii) For `-3 le x lt 1,` find the values of |x| (iv) For `-5 lt x lt 7 ` find the values of |x-2| (v) For `1 le x le 5` find fthe values of |2x -7| |
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Answer» (i) `2 lt x lt 4` i.e., values on real number line whose distance from zero lies between 2 and 4. Here values of x are positive `implies|x| in (2,4)` (ii) `-3 le x le -1` Here values on real number line whose distance from zero lies between 1 and 3 or equal to 1 or 3. `implies 1 le |x| le 3` (iii) ` -3 le x lt 1` For `-3 le x lt 0, |x| in (0,3]` For ` 0 le x lt 1, |x| in [0,1)` So for `-3 le x lt 1,|x| in [0,1)cup(0,3]" or " |x| in [0,3]` (iv) `-5 lt x lt 7` or `-7 lt x-2 lt 5` `implies 0 le |x-2| le 7` (v) `1 le x le 5` or `2 le2x le10` `implies -5 le 2x-7 le 3` `implies |2x-7| in[0,5]` |
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