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

Answer:

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

Step-by-step 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:

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