Step by step
The question
Question: solve |2x + 1| = 7.
|2x + 1| = 7
1 Two cases
The inside is 7 away from 0.
On the number line, 7 and minus 7 are both 7 away from 0.
So the inside is 7, or minus 7.
|A| = 7 → A = 7 or A = −7
7 and −7 are both 7 away from 0
Two small equations, side by side.
2x + 1 = 7 or 2x + 1 = −7
Careful!
Many people solve only 2x + 1 = 7.
Then they lose the second answer.
Careful: not only 2x + 1 = 7 ✗
2 Solve both
In each one, we take away 1 on both sides.
2x + 1 − 1 = 7 − 1 or 2x + 1 − 1 = −7 − 1
+ 1 and − 1 make zero, in both.
7 minus 1 is 6.
−7 minus 1 is −8.
2x = 6 or 2x = −8
To remove times 2, we divide by 2.
x = 62 or x = −82
So x = 3 or x = −4.
x = 3 or x = −4
3 Check
Let's check: put x = 3 in.
The inside is 7, and the bars make it 7.
x = 3: |2(3) + 1| = |7| = 7
Now put x = −4 in.
The inside is −7, and the bars make it 7.
x = −4: |2(−4) + 1| = |−7| = 7
Both give 7.
Both answers work!
Let's look back.
First: two cases.
Then: solve both.
Last: check.
Answer
x = 3 or x = −4