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If ⎪t+3⎪ > 5 which of the following could be the value of

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If ⎪t+3⎪ > 5 which of the following could be the value of [#permalink] New post 24 Jan 2016, 14:45
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63% (00:17) correct 36% (00:45) wrong based on 22 sessions
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

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Question: 21
Page: 462
Difficulty: medium


[Reveal] Spoiler: OA
A and F
[Reveal] Spoiler: OA

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Re: If ⎪t+3⎪ > 5 which of the following could be the value of [#permalink] New post 24 Jan 2016, 14:49
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Solution

⎪t+3⎪ > 5 is equal to \(t+3>5\) \(AND\) \(-t-3>5\)

From this we do have \(t>2\) \(AND\) \(t<-8\)

The answer is \(A\) and \(F\)
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Re: If ⎪t+3⎪ > 5 which of the following could be the value of [#permalink] New post 29 Jun 2018, 06:07
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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 positive


GIVEN: |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 > 2
So, 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 < -8
So, it's possible that t could equal -9 (answer choice A)

Answers: A and F

Cheers,
Brent
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Re: If ⎪t+3⎪ > 5 which of the following could be the value of   [#permalink] 29 Jun 2018, 06:07
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