Carcass wrote:

If |t+3| > 5, which of the following could be the value of t ?

Indicate \(all\) such values.

A −9

B −6

C −2

D 0

E 2

F 3

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: |t+3| > 5

This is in the form |

something| > k, so we'll apply Rule #2.

We get: EITHER t+3 > 5 OR t+3 < -5

If t+3 > 5, then we can subtract 3 from both sides to get:

t > 2So, it's possible that

t could equal 3 (answer choice F)

If t+3 < -5, then we can subtract 3 from both sides to get:

t < -8So, it's possible that

t could equal -9 (answer choice A)

Answers: A and F

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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