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