Step by step
The question
Question: solve |3x − 6| = 9.
|3x − 6| = 9
1 Two cases
The inside is 9 away from 0.
On the number line, 9 and minus 9 are both 9 away from 0.
So the inside is 9, or minus 9.
|A| = 9 → A = 9 or A = −9
9 and −9 are both 9 away from 0
Two small equations, side by side.
3x − 6 = 9 or 3x − 6 = −9
Careful!
Many people solve only 3x − 6 = 9.
Then they lose the second answer.
Careful: not only 3x − 6 = 9 ✗
2 Solve both
In each one, we add 6 on both sides.
3x − 6 + 6 = 9 + 6 or 3x − 6 + 6 = −9 + 6
− 6 and + 6 make zero, in both.
9 plus 6 is 15.
−9 plus 6 is −3.
3x = 15 or 3x = −3
To remove times 3, we divide by 3.
x = 153 or x = −33
So x = 5 or x = −1.
x = 5 or x = −1
3 Check
Let's check: put x = 5 in.
The inside is 9, and the bars make it 9.
x = 5: |3(5) − 6| = |9| = 9
Now put x = −1 in.
The inside is −9, and the bars make it 9.
x = −1: |3(−1) − 6| = |−9| = 9
Both give 9.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = 5 or x = −1