Step by step
The question
Question: solve |5 − x| = 2.
|5 − x| = 2
1 Two cases
The inside is 2 away from 0.
On the number line, 2 and minus 2 are both 2 away from 0.
So the inside is 2, or minus 2.
|A| = 2 → A = 2 or A = −2
2 and −2 are both 2 away from 0
Two small equations, side by side.
5 − x = 2 or 5 − x = −2
Careful!
Many people solve only 5 − x = 2.
Then they lose the second answer.
Careful: not only 5 − x = 2 ✗
2 Solve both
In each one, we take away 5 on both sides.
+ 5 and − 5 make zero, in both.
2 minus 5 is −3.
−2 minus 5 is −7.
−x = −3 or −x = −7
To remove times −1, we divide by −1.
x = −3−1 or x = −7−1
So x = 3 or x = 7.
x = 3 or x = 7
3 Check
Let's check: put x = 3 in.
The inside is 2, and the bars make it 2.
x = 3: |5 − 3| = |2| = 2
Now put x = 7 in.
The inside is −2, and the bars make it 2.
x = 7: |5 − 7| = |−2| = 2
Both give 2.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = 3 or x = 7