Step by step
The question
Question: solve |x + 7| = 3.
|x + 7| = 3
1 Two cases
The inside is 3 away from 0.
On the number line, 3 and minus 3 are both 3 away from 0.
So the inside is 3, or minus 3.
|A| = 3 → A = 3 or A = −3
3 and −3 are both 3 away from 0
Two small equations, side by side.
x + 7 = 3 or x + 7 = −3
Careful!
Many people solve only x + 7 = 3.
Then they lose the second answer.
Careful: not only x + 7 = 3 ✗
2 Solve both
In each one, we take away 7 on both sides.
x + 7 − 7 = 3 − 7 or x + 7 − 7 = −3 − 7
+ 7 and − 7 make zero, in both.
So x = −4 or x = −10.
x = −4 or x = −10
3 Check
Let's check: put x = −4 in.
The inside is 3, and the bars make it 3.
x = −4: |(−4) + 7| = |3| = 3
Now put x = −10 in.
The inside is −3, and the bars make it 3.
x = −10: |(−10) + 7| = |−3| = 3
Both give 3.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = −4 or x = −10