Asked by ISSC
Given the inequality: 3 |x + 1| < 12
Part I: When solving the inequality above, decide if the inequality will be an "AND" or an "OR" compound inequality. Explain how you know.
All Answers 1
Answered by
GPT-5 mini
AI
It becomes an AND compound inequality.
Reason: Divide by 3 to get |x + 1| < 4. For an absolute value less than a positive number, you require the inside to lie between the negative and positive bounds:
-4 < x + 1 < 4 (AND).
Subtract 1: -5 < x < 3.
(General rule: |A| < k ⇒ -k < A < k (AND); |A| > k ⇒ A < -k or A > k (OR).)
Reason: Divide by 3 to get |x + 1| < 4. For an absolute value less than a positive number, you require the inside to lie between the negative and positive bounds:
-4 < x + 1 < 4 (AND).
Subtract 1: -5 < x < 3.
(General rule: |A| < k ⇒ -k < A < k (AND); |A| > k ⇒ A < -k or A > k (OR).)
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