(i) 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 le 1,` find the values of `|x|`.
(iv) For `-5 lt x lt 7,` find the values of ` |x-2|`.
(iv) For `1 le x le 5,` find the values of `|2x-7|.`

Explanation

(i) `2 lt x lt 4`
Here values on real number line whose distance from zero lies between 2 and 4
Here values of x are positve `rArr |X| in (2,4)`
(ii) `-3 le x le -1`
Here value on real number line whose distance from zero lies between 1 and 3 or equal to 1 or 3 .
`rArr 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 0, |x| in {0,1)`
`So for -3 le x lt ,|X| in [0,1 ) cap (0,3 ] or |x| in [ 0,3]`
(iv) ` -5 lt x lt 7 `
` or -7 lt x -2 lt 5 `
`rArr 0 le |x-2|lt 7`
(v) `1 le x le 5`
of `2 le 2x le 10 `
`rArr -5 le 2x -7 le 3`
`rArr | 2x -7 | in [ 0, 5]`