Step by step
The question
Question: solve |x − 1| = 0.
|x − 1| = 0
1 One case
Only 0 is 0 away from 0.
So the inside is 0.
|A| = 0 → A = 0
One case only.
x − 1 = 0
2 Solve it
We add 1 on both sides.
x − 1 + 1 = 0 + 1
− 1 and + 1 make zero.
So x = 1.
x = 1
3 Check
Let's check: put x = 1 in.
The inside is 0, and the bars make it 0.
x = 1: |1 − 1| = |0| = 0
We get 0.
It works!
Let's look back.
First: one case.
Then: solve it.
Last: check.
Answer
x = 1