Solve |2x + 3| < 3
Absolute value inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −3 < x < 0 |
| Interval notation | (−3, 0) |
Step-by-step solution
5 steps-
1 Given\left|{2 x + 3}\right| < 3
Solve for x.
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2 |u| < d means u lies between −d and d
|u| is the distance from u to 0. Being less than 3 away from 0 means u lies between −3 and 3.
-3 < 2 x + 3 < 3 -
3 Subtract 3 from all three parts
A compound inequality is two inequalities at once. Doing the same operation to all three parts keeps both of them true, which isolates the variable in the middle.
-6 < 2 x < 0 -
4 Divide all three parts by 2-3 < x < 0
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5 Solution-3 < x < 0\qquad \left( -3, 0 \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| −2 | 1 | 3 | ✓ true |
| −4 | 5 | 3 | ✗ false |
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