Solve −8 < 2x + 4 ≤ 0
Compound inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −6 < x ≤ −2 |
| Interval notation | (−6, −2] |
Step-by-step solution
4 steps-
1 Given-8 < 2 x + 4 \le 0
Solve for x.
-
2 Subtract 4 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.
-12 < 2 x \le -4 -
3 Divide all three parts by 2-6 < x \le -2
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4 Solution-6 < x \le -2\qquad \left( -6, -2 \right]
Check with test values
| x | Left | Middle | Right | Holds? |
|---|---|---|---|---|
| −5 | −8 | −6 | 0 | ✓ true |
| −7 | −8 | −10 | 0 | ✗ false |
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