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The difference between the greatest and least possible values of n

10

A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

The difference between the greatest and least possible values of n

10

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know: Rule #1: If |something| < k, then –k < something < k Rule #2: If |something| > k, then EITHER something > k OR something < -k Note: these rules assume that k is positive

Given: |2n + 7| ≤ 10 In this case, we'll apply rule #1 to get: -10 ≤ 2n + 7 ≤ 10 Subtract 7 from all three parts: -17 ≤ 2n ≤ 3 Divide all three parts by 2 to get: -8.5 ≤ n ≤ 1.5 Since n is an INTEGER, the possible values of n are: -8, -7, -6, -5,....0, 1

The question: Quantity A: The difference between the greatest and least possible values of n Quantity B: 10

Re: The difference between the greatest and least possible value [#permalink]
28 Oct 2017, 00:32

2

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Little plot twist: if the inequality were \(|2n-7|\geq 10\), the solution would have been \(n \geq \frac{3}{2}\) and \(n \leq -\frac{17}{2}\). In this case the difference between the highest and smallest values of n would have been 2 - (-9) = 11 so that A would have been greater!