Step by step
The question
Question: solve |6 − 2x| = 4.
|6 − 2x| = 4
1 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.
|A| = 4 → A = 4 or A = −4
4 and −4 are both 4 away from 0
Two small equations, side by side.
6 − 2x = 4 or 6 − 2x = −4
Careful!
Many people solve only 6 − 2x = 4.
Then they lose the second answer.
Careful: not only 6 − 2x = 4 ✗
2 Solve both
In each one, we take away 6 on both sides.
+ 6 and − 6 make zero, in both.
4 minus 6 is −2.
−4 minus 6 is −10.
−2x = −2 or −2x = −10
To remove times −2, we divide by −2.
x = −2−2 or x = −10−2
So x = 1 or x = 5.
x = 1 or x = 5
3 Check
Let's check: put x = 1 in.
The inside is 4, and the bars make it 4.
x = 1: |6 − 2(1)| = |4| = 4
Now put x = 5 in.
The inside is −4, and the bars make it 4.
x = 5: |6 − 2(5)| = |−4| = 4
Both give 4.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = 1 or x = 5