ISEE Word Problems Question 285: Answer and Explanation

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Question: 285

4. A solution set is shown on the number line.

Which expression represents the solution set?

  • A. |x + 4| ≤ 6
  • B. |x + 4| ≤ –6
  • C. |x – 4| ≤ 6
  • D. |x – 4| ≤ –6

Correct Answer: C

Explanation:

C

Test the answers to determine which one yields the indicated graph. For each answer, there are two cases. For choice (A), first solve x + 4 ≤ 6. Subtract 4 from both sides: x ≤ 2. As this is not one of the indicated end points in the graph, eliminate choice (A). For choice (B), first solve x + 4 ≤ –6. Subtract 4 from both sides: x ≤ –10. As this is not one of the indicated end points in the graph, eliminate choice (B). For choice (C), first solve x – 4 ≤ 6. Add 4 to both sides: x ≤ 10. This is consistent with the graph. Now, solve x – 4 ≥ –6. Add 4 to both sides: x ≥ –2. This is also consistent with the graph, so choice (C) is correct.

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