Solve |2x − 6| < 3
Absolute value inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | 3/2 < x < 9/2 |
| Interval notation | (3/2, 9/2) |
Step-by-step solution
5 steps-
1 Given\left|{2 x - 6}\right| < 3
Solve for x.
-
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 - 6 < 3 -
3 Add 6 to 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.
3 < 2 x < 9 -
4 Divide all three parts by 2\frac{3}{2} < x < \frac{9}{2}
-
5 Solution\frac{3}{2} < x < \frac{9}{2}\qquad \left( \frac{3}{2}, \frac{9}{2} \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| 2 | 2 | 3 | ✓ true |
| 1 | 4 | 3 | ✗ false |
Open this problem in the solver
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.