PSAT Math Multiple-Choice Question 205: Answer and Explanation

Question: 205

Which symbol correctly completes the inequality whose solution is shown above?

• A. <
• B. >
• C. ≤
• D. ≥

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Heart of Algebra/Inequalities

Getting to the Answer: Apply logic to this question first and then algebra. The dot at the beginning of the shaded portion is an open dot, so -2 is not included in the solution set of the inequality. This means you can eliminate (C) and (D) because those symbols would include the endpoint. Don't immediately choose (B) just because the arrow is pointing to the right, which typically indicates greater than. When dealing with an inequality, if you multiply or divide by a negative number, you must flip the symbol, so the answer is not necessarily what you might think. Because you were able to eliminate two of the choices, the quickest approach is to pick one of the remaining symbols, plug it in, and see if it works. If it does, choose that answer. If it doesn't, then it must be the other symbol. Try (A):

The resulting inequality, x > -2, means all the values on the number line greater than (or to the right of) -2, so the initial inequality symbol must have been <. Choice (A) is correct.