Solve the following equation?

Question

$| | x - 2 | - 3 | < 5$ $||x-2|-3|<5$

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Answer 1 · 2018-07-28T17:22:07

$- 6 < x < 10$ $-6 < x < 10$

$| | x - 2 | - 3 | < 5$ $||x-2|-3|<5$ means

either $| x - 2 | - 3 < 5$ $|x-2|-3<5$ i.e. $| x - 2 | < 8$ $|x-2|<8$ ,

which means $x - 2 < 8$ $x-2<8$ i.e. $x < 10$ $x<10$

or $x - 2 > - 8$ $x-2> -8$ i.e. $x > - 6$ $x> -6$

which implies $- 6 < x < 10$ $-6 <x< 10$

or $| x - 2 | - 3 > - 5$ $|x-2|-3> -5$ i.e. $| x - 2 | > - 2$ $|x-2|> -2$

but this always true.

Hence answer is $- 6 < x < 10$ $-6 < x < 10$