Solve 0 < 2x + 3 ≤ 7
Compound inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −3/2 < x ≤ 2 |
| Interval notation | (−3/2, 2] |
Step-by-step solution
4 steps-
1 Given0 < 2 x + 3 \le 7
Solve for x.
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2 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.
-3 < 2 x \le 4 -
3 Divide all three parts by 2- \frac{3}{2} < x \le 2
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4 Solution- \frac{3}{2} < x \le 2\qquad \left( - \frac{3}{2}, 2 \right]
Check with test values
| x | Left | Middle | Right | Holds? |
|---|---|---|---|---|
| −1 | 0 | 1 | 7 | ✓ true |
| −2 | 0 | −1 | 7 | ✗ false |
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