Question

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

Answer 1

`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`.