Question

Solve each equation. Check your solutions.
5 - 3|2 + 2w|= -7

Answer 1

5-3(2+2w)=-7
5-6-6w=-7
-6w=-7-5+6
-6w=-6
w=1

Answer 2

`w=1\text{ or } w=-3`

Explanation:

So we have the equation:

`5-3|2+2w|=-7`

First, subtract 5 from both sides:

`-3|2+2w|=-12`

Divide both sides by -3:

`|2+2w|=4`

Definition of Absolute Value:

`2+2w=4\text{ or } 2+2w=-4`

Divide both sides of the equation by 2 for both equations:

`1+w=2\text{ or } 1+w=-2`

Subtract 1 from both sides:

`w=1\text{ or } w=-3`

And we're done!

To check:

`5-3|2+2(1)|=-7`

Multiply:

`5-3|2+2|=-7`

Add:

`5-3|4|=-7`

Multiply:

`5-12=-7`

Subtract:

`-7\stackrel{\checkmark}{=}-7`

And:

`5-3|2+2(-3)|=-7`

Multiply:

`5-3|2-6|=-7`

Subtract:

`5-3|-4|=-7`

Absolute Value:

`5-3(4)=-7`

Multiply:

`5-12=-7`

Subtract:

`-7\stackrel{\checkmark}{=}-7`