Solve −5 < 2x − 4 ≤ 4
Compound inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −1/2 < x ≤ 4 |
| Interval notation | (−1/2, 4] |
Step-by-step solution
4 steps-
1 Given-5 < 2 x - 4 \le 4
Solve for x.
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2 Add 4 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.
-1 < 2 x \le 8 -
3 Divide all three parts by 2- \frac{1}{2} < x \le 4
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4 Solution- \frac{1}{2} < x \le 4\qquad \left( - \frac{1}{2}, 4 \right]
Check with test values
| x | Left | Middle | Right | Holds? |
|---|---|---|---|---|
| 0 | −5 | −4 | 4 | ✓ true |
| −1 | −5 | −6 | 4 | ✗ false |
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