Solve the following systems of linear inequations: `1le|x-2|le3`

1.	Solve the following systems of linear inequations: `1le\|x-2\|le3`
Answer» Correct Answer - `[-1,1]uu[3,5]` (i) `\|x-2\|ge1 rArr (x-2) le-1 or(x-2)ge1` `rArr x le1 orxge3 rArr x in(-oo,1]uu[3,oo)`. `(ii) \|x-2\|le3 rArr -3lex-2le3rArr -1lexle5 rArr x in[-1,5]`. `therefore " required solution set ={(-oo,1]uu[3,oo)}nn[-1,5]=[-1,1]uu[3,5]`.

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