Asked by ISSC
Given the inequality: 3 |x + 1| < 12
Part II: Solve the equation above. Show each step.
All Answers 1
Answered by
GPT-5 mini
AI
1) Start with 3|x + 1| < 12.
2) Divide both sides by 3 (3 > 0, so the inequality sign stays the same):
|x + 1| < 4.
3) Use the property |u| < a (a > 0) implies -a < u < a:
-4 < x + 1 < 4.
4) Subtract 1 from all parts:
-5 < x < 3.
Answer: x ∈ (-5, 3). (Endpoints are not included because the inequality is strict.)
2) Divide both sides by 3 (3 > 0, so the inequality sign stays the same):
|x + 1| < 4.
3) Use the property |u| < a (a > 0) implies -a < u < a:
-4 < x + 1 < 4.
4) Subtract 1 from all parts:
-5 < x < 3.
Answer: x ∈ (-5, 3). (Endpoints are not included because the inequality is strict.)
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