ISEE Word Problems Question 191: Answer and Explanation
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Question: 191
2. Which describes all values of x for which |3x – 4| ≥ 8?
- A. x ≤ -
or x ≥ 4 - B. x ≥ or x ≤ -4
- C. x ≤
- D. x ≥ 4
Correct Answer: A
Explanation:
The answer is A
You need to solve for two cases. First, solve 3x - 4 ≥ 8. Add 4 to each side: 3x ≥ 12. Divide both sides by 3: x ≥ 4. Now solve 3x - 4 ≤ -8. Add 4 to each side: 3x ≤ -4. Divide both sides by 3: x ≤ - . As the two results are not connected on the number line, the result is x ≤ - or x ≥ 4.
With absolute value inequalities, there are always two solutions, so you can eliminate choices (C) and (D). If you ignore the absolute value and solve, you will get x ≥ 4. Only one answer choice has this value.