Step by step
The question
Question: solve |2x| = 10.
|2x| = 10
1 Two cases
The inside is 10 away from 0.
On the number line, 10 and minus 10 are both 10 away from 0.
So the inside is 10, or minus 10.
|A| = 10 → A = 10 or A = −10
10 and −10 are both 10 away from 0
Two small equations, side by side.
2x = 10 or 2x = −10
Careful!
Many people solve only 2x = 10.
Then they lose the second answer.
Careful: not only 2x = 10 ✗
2 Solve both
To remove times 2, we divide by 2.
x = 102 or x = −102
So x = 5 or x = −5.
x = 5 or x = −5
3 Check
Let's check: put x = 5 in.
The inside is 10, and the bars make it 10.
x = 5: |2(5)| = |10| = 10
Now put x = −5 in.
The inside is −10, and the bars make it 10.
x = −5: |2(−5)| = |−10| = 10
Both give 10.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = 5 or x = −5