Asked by ISSC
Given the inequality: 3 |x + 1| < 12
Part II: Solve the equation above. Show and/or explain each step.
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Answered by
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Solve 3|x + 1| < 12.
1. Divide both sides by 3 (3 > 0, so inequality direction stays the same):
|x + 1| < 4.
2. Use the definition of absolute value: |A| < b (b > 0) is equivalent to −b < A < b. Here A = x + 1 and b = 4:
−4 < x + 1 < 4.
3. Subtract 1 from all parts:
−5 < x < 3.
Solution set: {x | −5 < x < 3}, or in interval notation: (−5, 3).
(Check: x = 0 gives 3|1| = 3 < 12 (true); x = −5 or x = 3 gives 12, which is not < 12, so endpoints are excluded.)
1. Divide both sides by 3 (3 > 0, so inequality direction stays the same):
|x + 1| < 4.
2. Use the definition of absolute value: |A| < b (b > 0) is equivalent to −b < A < b. Here A = x + 1 and b = 4:
−4 < x + 1 < 4.
3. Subtract 1 from all parts:
−5 < x < 3.
Solution set: {x | −5 < x < 3}, or in interval notation: (−5, 3).
(Check: x = 0 gives 3|1| = 3 < 12 (true); x = −5 or x = 3 gives 12, which is not < 12, so endpoints are excluded.)
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