Step by step
The question
Question: solve |2x − 5| + 1 = 8.
1 Get the bars alone
We want the bars by themselves.
The + 1 is in the way, so we take away 1 on both sides.
+ 1 and − 1 make zero.
Cross them out.
8 minus 1 is 7.
2 Two cases
The inside is 7 away from 0.
On the number line, 7 and minus 7 are both 7 away from 0.
So the inside is 7, or minus 7.
Two small equations, side by side.
Careful!
Many people solve only 2x − 5 = 7.
Then they lose the second answer.
3 Solve both
In each one, we add 5 on both sides.
− 5 and + 5 make zero, in both.
7 plus 5 is 12.
−7 plus 5 is −2.
To remove times 2, we divide by 2.
So x = 6 or x = −1.
4 Check
Let's check: put x = 6 in.
The inside is 7, and the bars make it 7.
Now put x = −1 in.
The inside is −7, and the bars make it 7.
Both give 8.
Both answers work!
Let's look back.
First: get the bars alone.
Then: two cases.
Then: solve both.
Last: check.