Solve −4 < 2x + 5 ≤ 2
Compound inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −9/2 < x ≤ −3/2 |
| Interval notation | (−9/2, −3/2] |
Step-by-step solution
4 steps-
1 Given-4 < 2 x + 5 \le 2
Solve for x.
-
2 Subtract 5 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.
-9 < 2 x \le -3 -
3 Divide all three parts by 2- \frac{9}{2} < x \le - \frac{3}{2}
-
4 Solution- \frac{9}{2} < x \le - \frac{3}{2}\qquad \left( - \frac{9}{2}, - \frac{3}{2} \right]
Check with test values
| x | Left | Middle | Right | Holds? |
|---|---|---|---|---|
| −4 | −4 | −3 | 2 | ✓ true |
| −5 | −4 | −5 | 2 | ✗ 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.