Official Guide Explanation:
Problem Solving #173




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Solution and Metadata

Question: 173
Page: 176
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other
Category 2: Arithmetic > Real Numbers >

Explanation: First, simplify the inequality. Add x2 to both sides: 1 ≥ x2. Since x2 cannot be negative (no number squared is negative) we can say that 0 ≤ x2 ≤ 1. The only way x2 can be within that range is if x itself is within that range, or within the negative equivalent of that range. For example, if x = (1/2), x2 = (1/4). If x= - (1/2), x2 = (1/4). So, the inequality that expresses the possible range of x is -1 ≤ x ≤ 1, choice (E).

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