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