Question

Solve for w. | – w|≥2 Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form.

Answer 1

`-2 \geq w \geq 2`

Explanation:

Given

`|-w| \geq 2`

Required

Solve for w

`|-w| \geq 2`

In absolution functions;

`|-w| = |w|`

So, the given expression can be rewritten as

`|w| \geq 2`

Removing the absolute sign, will gibe

`w \geq 2` or
`w \leq -2`

When the second inequality os rewritten, it gives

`w \geq 2` or
`-2 \geq w`

Reorder both inequalities

`-2 \geq w` or
`w \geq 2`

Lastly, both inequalities are combined

`-2 \geq w \geq 2`