Solve −5 < 2x − 1 ≤ 9
Compound inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −2 < x ≤ 5 |
| Interval notation | (−2, 5] |
Step-by-step solution
4 steps-
1 Given-5 < 2 x - 1 \le 9
Solve for x.
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2 Add 1 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.
-4 < 2 x \le 10 -
3 Divide all three parts by 2-2 < x \le 5
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4 Solution-2 < x \le 5\qquad \left( -2, 5 \right]
Check with test values
| x | Left | Middle | Right | Holds? |
|---|---|---|---|---|
| −1 | −5 | −3 | 9 | ✓ true |
| −3 | −5 | −7 | 9 | ✗ false |
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