# What is the solution to the inequality absx > 6?

May 13, 2018

$x > 6$ or $x < - 6$

#### Explanation:

If you consider any number $x > 6$, the inequality is trivially solved: you have $| x | = x$, and you're choosing a number bigger than $6$ in the first place.

If instead you consider some number $x < - 6$, then $| x | = - x$, and so you go back to the first case

For example, if you choose $x = 17$ you're in the trivial case: $| 17 | = 17$, and $17 > 6$.

If instead you choose $x = - 20$, you have $| - 20 | = 20$, and $20 > 6$.