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Which of the options must be true if x satisfies the 2 inequalities gi

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Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

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New post 05 Mar 2019, 07:16
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A
B
C
D
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Which of the options must be true if x satisfies the 2 inequalities given below?

((5x−1)/(x+3))<1 and |2x − 5| ≤ 5?

x < 0
x > 0
x < 2
x > 2
None of the above
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Re: Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

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New post 05 Mar 2019, 09:20
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Kindly submit the answer

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Re: Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

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New post 05 Mar 2019, 10:21
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The two inequalities must be verified at the same time. Let's take into account the first one:

\(\frac{5x - 1}{x + 3}< 1\)
\(\frac{5x - 1 - x - 3}{x + 3} < 0\)
\(\frac{4x - 4}{x + 3} < 0\)

\(Numerator: x ≥ 1\)
\(Denominator: x > - 3\)

So, it will be negative in the range \((-3,1]\)

Let's consider the second one:

\(|2x - 5| ≤ 5\)
\(-5 ≤ 2x - 5 ≤ 5\)
\(0 ≤ x ≤ 5\)

So, the range is \([0, 5]\)

Put these outputs together to assess the values for which \(x\) is verified in both.

This happens when \(0 ≤ x ≤ 1\)

You reject all options except C.
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Re: Which of the options must be true if x satisfies the 2 inequalities gi  [#permalink]

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New post 22 May 2019, 06:03
1
lucajava wrote:
The two inequalities must be verified at the same time. Let's take into account the first one:

\(\frac{5x - 1}{x + 3}< 1\)
\(\frac{5x - 1 - x - 3}{x + 3} < 0\)
\(\frac{4x - 4}{x + 3} < 0\)

\(Numerator: x ≥ 1\)
\(Denominator: x > - 3\)

So, it will be negative in the range \((-3,1]\)

Let's consider the second one:

\(|2x - 5| ≤ 5\)
\(-5 ≤ 2x - 5 ≤ 5\)
\(0 ≤ x ≤ 5\)

So, the range is \([0, 5]\)

Put these outputs together to assess the values for which \(x\) is verified in both.

This happens when \(0 ≤ x ≤ 1\)

You reject all options except C.


Hi,
how does option C x<2 satisfy our expected range of 0<=x<1?
As per x<2, x can be -1 which is not in our range.
Thanks!
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Re: Which of the options must be true if x satisfies the 2 inequalities gi   [#permalink] 22 May 2019, 06:03
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