Carcass wrote:

If \(| x + 1 | \leq 5\) and \(|y — 1| \leq 5\), what is the least possible value of the product \(xy\) ?

Enter your value 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 positiveGIVEN: |x + 1| ≤ 5

From Rule #1 above, we can write: -5 ≤ x + 1 ≤ 5

Subtract 1 from all sides to get: -6 ≤ x ≤ 4

So, x can be ANY value from -6 to 4 INCLUSIVE

GIVEN: |y - 1| ≤ 5

From Rule #1 above, we can write: -5 ≤ y - 1 ≤ 5

Add 1 to all sides to get: -4 ≤ y ≤ 6

So, y can be ANY value from -4 to 6 INCLUSIVE

What is the least possible value of the product xy? The LEAST product will be NEGATIVE

So, one value (x or y) must be POSITIVE, and the other value must be NEGATIVE

The LEAST product occurs when x = -6 and y = 6

So, the least product = (-6)(6) = -36

Answer: -36

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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