Official Guide Explanation:
Problem Solving #92




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Solution and Metadata

Question: 92
Page: 73
Difficulty: 5 (Moderate)
Category 1: Algebra > Inequalities > other
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: If you're given an inequality and you need to find what it implies about another variable, see what happens when the first variable is at the limit of its inequality. In this case, that means finding out what happens in the equation, when b = 2.

2x - 3(2) = 0

2x = 6

x = 3

That doesn't mean that (C) is right (necessarily), just that 3 is the boundary line. So (C), (D), or (E) must be right. To find out which one, use another number for b that fits the constraints of the inequality, such as b = 1:

2x - 3(1) = 0

2x = 3

x = (3/2)

Since x could be equal to (3/2), the inequality must allow for x to be less than 3, so (D) must be correct.

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