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## Official Guide Explanation:Problem Solving #130

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 130
Page: 170
Difficulty: 5 (Moderate)
Category 1: Geometry > Lines >
Category 2: Algebra > Inequalities > other
Category 3: Algebra > Absolute Value >

Explanation: Recognize that any equation that includes absolute value symbols implies two separate equations: one when the expression inside the absolute value signs is positive, one when it's negative. The number line indicates that you're looking for the expression that gives you the two equations x ≤ 3 and x ≥ -5. (A) and (B) can be eliminated, because those will give you 3 and -3 and 5 and -5 as the endpoints. Try the remaining choices:

(C): positive: x - 2 ≤ 3, or x ≤ 5. That's not one of the ones we need, so we can stop there.

(D): positive: x - 1 ≤ 4, or x ≤ 5. Same problem. At this point, you probably don't need to check (E) to know that it's correct, but I'll show the solution for the sake of completeness.

(E): positive: x + 1 ≤ 4, or x ≤ 3

negative: -(x + 1) ≤ 4, or x + 1 ≥ -4, or x ≥ -5

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