Step by step
The question
Question: solve 3|x| − 4 = 8.
1 Get the bars alone
We want the bars by themselves.
The − 4 is in the way, so we add 4 on both sides.
− 4 and + 4 make zero.
Cross them out.
8 plus 4 is 12.
To remove times 3, we divide both sides by 3.
3 divided by 3 is 1.
So just the bars is left.
12 divided by 3 is 4.
2 Two cases
The inside is 4 away from 0.
On the number line, 4 and minus 4 are both 4 away from 0.
So the inside is 4, or minus 4.
Two small equations, side by side.
Careful!
Many people solve only x = 4.
Then they lose the second answer.
3 Solve both
So x = 4 or x = −4.
4 Check
Let's check: put x = 4 in.
The inside is 4, and the bars make it 4.
Now put x = −4 in.
The inside is −4, and the bars make it 4.
Both give 8.
Both answers work!
Let's look back.
First: get the bars alone.
Then: two cases.
Then: solve both.
Last: check.