Question

How do you solve `2| w + 6| \geq 18`?

Answer 1

`w\le-15` or `w\ge3`

Explanation:

First isolate the absolute value.
`(\cancel(2)|w+6|)/(\cancel(color(red)(2)))\ge18/\color(red)(2)`
`|w+6|\ge9`

Absolute value rule: `|a+b|\ltc` becomes `-c\lt(a+b)\ltc`

`\therefore(w+6)\le-9` or `(w+6)\ge9`
`\color(white)(♦)w\le-9-6` or `w\ge9-6`

`\rArr`result: `w\le-15` or `w\ge3`