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Which of the following expresses the range of possible values for

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Which of the following expresses the range of possible values for  [#permalink]

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New post 08 Jan 2017, 08:09
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Which of the following expresses the range of possible values for t if 0 < |5t − 8| < 1?

A. 2/5 < t < 14/5
B. 2/5 < t < 9/5
C. 7/5 < t < 14/5
D. 7/5 < t < 9/5
E. 9/5 < t < 14/5

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Re: Which of the following expresses the range of possible values for  [#permalink]

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New post 08 Jan 2017, 11:08
Bunuel wrote:
Which of the following expresses the range of possible values for t if 0 < |5t − 8| < 1?

A. 2/5 < t < 14/5
B. 2/5 < t < 9/5
C. 7/5 < t < 14/5
D. 7/5 < t < 9/5
E. 9/5 < t < 14/5


if we put t=8/5 which is included in option A-D
then inequality doesnt hold

for E again value is greater than defined range 0 < |5t − 8| < 1

I m not getting the answer
Could any one help!!

Bunuel
is everything right with the Question??
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Re: Which of the following expresses the range of possible values for  [#permalink]

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New post 08 Jan 2017, 19:02
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Bunuel wrote:
Which of the following expresses the range of possible values for t if 0 < |5t − 8| < 1?

A. 2/5 < t < 14/5
B. 2/5 < t < 9/5
C. 7/5 < t < 14/5
D. 7/5 < t < 9/5
E. 9/5 < t < 14/5


Solve for the inequality \(0 < |5t − 8| < 1\)

\(|5t − 8| > 0 \implies t \neq \frac{8}{5}\)

\(|5t − 8| < 1 \implies -1 < 5t-8 < 1 \implies 7 < 5t < 9 \implies \frac{7}{5} < t < \frac{9}{5}\)

It seems that there is no answer satisfied the inequality.

The answer will be D if the condition \(0 < |5t − 8|\) doesn't exist in the inequality.
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Re: Which of the following expresses the range of possible values for  [#permalink]

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New post 08 Jan 2017, 20:06
Bunuel wrote:
Which of the following expresses the range of possible values for t if 0 < |5t − 8| < 1?

A. 2/5 < t < 14/5
B. 2/5 < t < 9/5
C. 7/5 < t < 14/5
D. 7/5 < t < 9/5
E. 9/5 < t < 14/5


Whenever we have modulus of this kind, the value inside MOD will be NEGATIVE and positive both, so a range will take 0 also unless specified..

Here 5t-8 will be NEGATIVE , -1, at 7/5 and POSITIVE,1, at 9/5..
And 0 at 8/5

So the range becomes 7/5 to 9/5..
However it should not consist of 8/5..
And ans should be 7/5<T<9/5, where T is not equal to 8/5..
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Re: Which of the following expresses the range of possible values for  [#permalink]

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New post 12 Nov 2017, 11:19
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|5t-8| < 1 or |5t-8| >0

Solving these we get,
\(t<\frac{9}{5}\) or \(t>\frac{7}{5}\) for the first equation

The second equation yields \(t >\frac{8}{5}\) or \(\frac{8}{5}>t\), which is nonsensical.

Hence answer is D
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Which of the following expresses the range of possible values for  [#permalink]

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New post 27 Feb 2018, 06:13
broall wrote:
Bunuel wrote:
Which of the following expresses the range of possible values for t if 0 < |5t − 8| < 1?

A. 2/5 < t < 14/5
B. 2/5 < t < 9/5
C. 7/5 < t < 14/5
D. 7/5 < t < 9/5
E. 9/5 < t < 14/5


Solve for the inequality \(0 < |5t − 8| < 1\)

\(|5t − 8| > 0 \implies t \neq \frac{8}{5}\)

\(|5t − 8| < 1 \implies -1 < 5t-8 < 1 \implies 7 < 5t < 9 \implies \frac{7}{5} < t < \frac{9}{5}\)

It seems that there is no answer satisfied the inequality.

The answer will be D if the condition \(0 < |5t − 8|\) doesn't exist in the inequality.


Broall, how do you know to drop the modulus and make the outliers -1 and 1? For me, I originally came up with \(\frac{8}{5}\)<t<\(\frac{9}{5}\). I just added 8 to both sides and then divided by 5. What is wrong with this solution and how should I approach questions like this in the future?

Thanks,
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Re: Which of the following expresses the range of possible values for  [#permalink]

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New post 27 Feb 2018, 06:33
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|5t-8|<1

You have to calculate this for the 2 situations of when 5t-8 is positive and when 5t-8 is negative

when 5t-8 is +ve, |5t-8| = 5t-8
therefore, 5t-8<1 => t<9/5

when 5t-8 is -ve, |5t-8| = -(5t-8)
therefore, -(5t-8)<1 => 5t-8>-1 => t>7/5

the direct step for this sort of problems

|x|<y, then -y<x<y
|x|>y, then -y>x>y
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  [#permalink]

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New post 27 Feb 2018, 07:51
rkishores051 wrote:
|5t-8|<1

You have to calculate this for the 2 situations of when 5t-8 is positive and when 5t-8 is negative

when 5t-8 is +ve, |5t-8| = 5t-8
therefore, 5t-8<1 => t<9/5

when 5t-8 is -ve, |5t-8| = -(5t-8)
therefore, -(5t-8)<1 => 5t-8>-1 => t>7/5

the direct step for this sort of problems

|x|<y, then -y<x<y
|x|>y, then -y>x>y


Great description, thanks man!
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&nbs [#permalink] 27 Feb 2018, 07:51
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