Question

How do you solve and write the following in interval notation: `| 3 − 2x | − 8 ≥ 1`?

Answer 1

`x<=-3` or `x>=6`

Explanation:

`|3-2x|-8>=1` means `|3-2x|>=9`

Now `|a|>=b` means either `a>=b` or `-a>=b`

Hence, `|3-2x|>=9` means

either `3-2x>=9` i.e. `-2x>=9-3` or `-2x>=6` i.e. `x<=-3`

or `-(3-2x)>=9` i.e. `-3+2x>=9` or `2x>=12` i.e. `x>=6`