Step by step
The question
Question: solve |x − 6| = 6.
|x − 6| = 6
1 Two cases
The inside is 6 away from 0.
On the number line, 6 and minus 6 are both 6 away from 0.
So the inside is 6, or minus 6.
|A| = 6 → A = 6 or A = −6
6 and −6 are both 6 away from 0
Two small equations, side by side.
x − 6 = 6 or x − 6 = −6
Careful!
Many people solve only x − 6 = 6.
Then they lose the second answer.
Careful: not only x − 6 = 6 ✗
2 Solve both
In each one, we add 6 on both sides.
x − 6 + 6 = 6 + 6 or x − 6 + 6 = −6 + 6
− 6 and + 6 make zero, in both.
So x = 12 or x = 0.
x = 12 or x = 0
3 Check
Let's check: put x = 12 in.
The inside is 6, and the bars make it 6.
x = 12: |12 − 6| = |6| = 6
Now put x = 0 in.
The inside is −6, and the bars make it 6.
x = 0: |0 − 6| = |−6| = 6
Both give 6.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = 12 or x = 0