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|

Explanation

(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]`