Step by step
The question
Question: solve |3x + 1| = 2.
|3x + 1| = 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.
3x + 1 = 2 or 3x + 1 = −2
Careful!
Many people solve only 3x + 1 = 2.
Then they lose the second answer.
Careful: not only 3x + 1 = 2 ✗
2 Solve both
In each one, we take away 1 on both sides.
3x + 1 − 1 = 2 − 1 or 3x + 1 − 1 = −2 − 1
+ 1 and − 1 make zero, in both.
2 minus 1 is 1.
−2 minus 1 is −3.
3x = 1 or 3x = −3
To remove times 3, we divide by 3.
x = 13 or x = −33
So x = 1/3 or x = −1.
x = 13 or x = −1
3 Check
Let's check: put x = 1/3 in.
The inside is 2, and the bars make it 2.
x = 13: |3(13) + 1| = |2| = 2
Now put x = −1 in.
The inside is −2, and the bars make it 2.
x = −1: |3(−1) + 1| = |−2| = 2
Both give 2.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = 13 or x = −1