Solve 2 < 2x + 5 ≤ 8
Compound inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −3/2 < x ≤ 3/2 |
| Interval notation | (−3/2, 3/2] |
Step-by-step solution
4 steps-
1 Given2 < 2 x + 5 \le 8
Solve for x.
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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.
-3 < 2 x \le 3 -
3 Divide all three parts by 2- \frac{3}{2} < x \le \frac{3}{2}
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4 Solution- \frac{3}{2} < x \le \frac{3}{2}\qquad \left( - \frac{3}{2}, \frac{3}{2} \right]
Check with test values
| x | Left | Middle | Right | Holds? |
|---|---|---|---|---|
| −1 | 2 | 3 | 8 | ✓ true |
| −2 | 2 | 1 | 8 | ✗ false |
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