Solve |2x + 0| < 2
Absolute value inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −1 < x < 1 |
| Interval notation | (−1, 1) |
Step-by-step solution
4 steps-
1 Given\left|{2 x + 0}\right| < 2
Solve for x.
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2 Isolate the absolute value\left|{x}\right| < 1
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3 |u| < d means u lies between −d and d
|u| is the distance from u to 0. Being less than 1 away from 0 means u lies between −1 and 1.
-1 < x < 1 -
4 Solution-1 < x < 1\qquad \left( -1, 1 \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| 0 | 0 | 2 | ✓ true |
| −2 | 4 | 2 | ✗ false |
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