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Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between

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Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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New post 18 Oct 2016, 02:24
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A
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E

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Question Stats:

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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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New post 18 Oct 2016, 02:40
2x+7>5

2x>-2

x>-1

5x-13<7

5x<20

x<4

B


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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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New post 18 Oct 2016, 04:45
Bunuel wrote:
Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5



From the first inequality,

\(2x + 7 > 5\)

\(x > -1\)

From the second inequality,

\(5x - 13 < 7\)

\(x <\) \(\frac{20}{5}\)

\(x < 4\) approx

Therefor (B) \(-1 < x < 4\)
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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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New post 18 Oct 2016, 06:07
Bunuel wrote:
Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5


2x + 7 > 5
i.e 2x >5-7
i.e. 2x > -2
i.e. x > -1

Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4

i.e. -1 < x < 4

Answer: Option B
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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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New post 18 Oct 2016, 07:42
Bunuel wrote:
Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5


Min value of x in 2x + 7 > 5 must be -

2x > -2

Or, x > - 1

Max value of x in 5x - 13 < 7 must be -

5x < 20

Or, x < 4

So, x must be between -1 and 4 , and answer will hence be (B)

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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between  [#permalink]

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New post 14 Jan 2018, 11:25
Bunuel wrote:
Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?

A. -4 and -1
B. -1 and 4
C. -4 and 1
D. -2 and 5
E. 2 and 5


\(2x + 7 > 5\)

Or, \(2x > -2\)

Or, \(x > -1\)

\(5x - 13 < 7\)

Or, \(5x < 20\)

Or, \(x < 4\)

Finally we have : \(-1 < x < 4\), among the given options only (B) satisfies, answer will be (B)
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Re: Given that 2x + 7 > 5 and 5x - 13 < 7, all values of x must be between   [#permalink] 14 Jan 2018, 11:25
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