# Solve the following equation?

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

Jul 28, 2018

$- 6 < x < 10$

#### Explanation:

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

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

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

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

which implies $- 6 < x < 10$

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

but this always true.

Hence answer is $- 6 < x < 10$