Step by step
The question
Question: solve |4x + 2| = 6.
|4x + 2| = 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.
4x + 2 = 6 or 4x + 2 = −6
Careful!
Many people solve only 4x + 2 = 6.
Then they lose the second answer.
Careful: not only 4x + 2 = 6 ✗
2 Solve both
In each one, we take away 2 on both sides.
4x + 2 − 2 = 6 − 2 or 4x + 2 − 2 = −6 − 2
+ 2 and − 2 make zero, in both.
6 minus 2 is 4.
−6 minus 2 is −8.
4x = 4 or 4x = −8
To remove times 4, we divide by 4.
x = 44 or x = −84
So x = 1 or x = −2.
x = 1 or x = −2
3 Check
Let's check: put x = 1 in.
The inside is 6, and the bars make it 6.
x = 1: |4(1) + 2| = |6| = 6
Now put x = −2 in.
The inside is −6, and the bars make it 6.
x = −2: |4(−2) + 2| = |−6| = 6
Both give 6.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = 1 or x = −2