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If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu

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Bunuel
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If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu [#permalink] New post   09 Jun 2020, 06:51
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If \(4x + 2 < x^2 + 3x − 18 < 0\), where x is an integer, what is the value of x ?

A. -6
B. -5
C. -4
D. 6
E. 7
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B
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nick1816
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Re: If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu [#permalink] New post   09 Jun 2020, 08:09
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\(4x + 2 < x^2 + 3x − 18\)

\(x^2-x -20 >0\)

\((x-5)(x+4)> 0\)

x>5 or x<-4........(1)

\(x^2 + 3x − 18 < 0\)

\((x+6)(x-3)<0\)

-6<x<3......(2)

From (1) and (2)

x = -5





Bunuel wrote:
If \(4x + 2 < x^2 + 3x − 18 < 0\), where x is an integer, what is the value of x ?

A. -6
B. -5
C. -4
D. 6
E. 7
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If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu [#permalink] New post   09 Jun 2020, 08:13
Bunuel wrote:
If \(4x + 2 < x^2 + 3x − 18 < 0\), where x is an integer, what is the value of x ?

A. -6
B. -5
C. -4
D. 6
E. 7


Asked: If \(4x + 2 < x^2 + 3x − 18 < 0\), where x is an integer, what is the value of x ?

\(4x + 2 < x^2 + 3x − 18 < 0\)
x^2 - x - 20 >0
(x-5)(x+4)<0
x<-4 or x>5

4x + 2 < 0
x < - 1/2

x^2 + 3x -18<0
(x+6)(x-3)<0
-6<x<3

x = - 5 satisfies all 3 conditions

IMO B
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Re: If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu [#permalink] New post   09 Jun 2020, 09:01
4x+2<x^2+3x-18<0

Put values from option one by one
A. X = -6
=> 4x+2<x^2+3x-18<0
=> 4(-6)+2<(-6)^2+3(-6)-18<0
=> -24+2<36-18-18<0
=> -22<0=0 (not satisfying)

B. X = -5
=> 4x+2<x^2+3x-18<0
=> 4(-5)+2<(-5)^2+3(-5)-18<0
=> -20+2<25-15-18<0
=> -18<-8<0 (Satisfying)

C. X = -4
=> 4x+2<x^2+3x-18<0
=> 4(-4)+2<(-4)^2+3(-4)-18<0
=> -16+2<16-12-18<0
=> -14=-14<0 (not satisfying)

D. X = +6
=> 4x+2<x^2+3x-18<0
=> 4(6)+2<(6)^2+3(6)-18<0
=> 24+2<36+18-18<0
=> 26<36>0 (not satisfying)

E. X = +7
=> 4x+2<x^2+3x-18<0
=> 4(7)+2<(7)^2+3(7)-18<0
=> 28+2<49+21-18<0
=> 30<52>0 (not satisfying)

Answer is B

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Re: If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu [#permalink] New post   09 Jun 2020, 12:21
IMO :- -5 Should be Ans

One way of Solving this question is by Splitting the Quadratic equation and then Comparing
While another way is through the graph


One will be a Parabolic Graph, while another will be line graph

Both will Join at (-5,-8), while the line will have x-intercept as -1

As per requirement value of Parabola Must be less than 1 while Greater than Value of the line

Find attached Image
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Re: If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu [#permalink] New post   11 Jun 2020, 13:52
Expert Reply
Bunuel wrote:
If \(4x + 2 < x^2 + 3x − 18 < 0\), where x is an integer, what is the value of x ?

A. -6
B. -5
C. -4
D. 6
E. 7


Solution:

Instead of solving the inequality algebraically, we can just solve it by checking the given choices. Notice that we can eliminate choices D and E since 4x + 2 would not be less than 0 if we use the values in those choices for x.

A. -6

4x + 2 = -24 + 2 = -22

x^2 + 3x - 18 = 36 - 18 - 18 = 0

Since x^2 + 3x - 18 is not less than 0 when x = -6, choice A is not the correct answer.

B. -5

4x + 2 = -20 + 2 = -18

x^2 + 3x - 18 = 25 - 15 - 18 = -8

We see that both expressions yield a negative value when x = -5, and the former is less than the latter, so choice B is the correct answer.

Answer: B
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Re: If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu [#permalink] New post   11 Jun 2020, 20:47
Hi ScottTargetTestPrep,

Please confirm if my understanding is correct:
We don't need to check for x = -4, since PS questions will always have only 1 correct answer. We already obtained that B satisfies the equation, so we can skip check for C.

Thanks
Lipun
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Re: If 4x + 2 < x^2 + 3x − 18 < 0, where x is an integer, what is the valu [#permalink] New post   29 Jun 2020, 09:01
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Lipun wrote:
Hi ScottTargetTestPrep,

Please confirm if my understanding is correct:
We don't need to check for x = -4, since PS questions will always have only 1 correct answer. We already obtained that B satisfies the equation, so we can skip check for C.

Thanks
Lipun


Response to Lipun:

Your understanding is correct. We have already found one value for x which satisfies 4x + 2 < x^2 + 3x - 18 < 0 and this means that the values in every other answer choice will either not satisfy 4x + 2 < x^2 + 3x - 18 or not satisfy x^2 + 3x - 18 < 0. If there were a value of x besides x = -5 among the answer choices satisfying both inequalities, that answer choice would be another correct answer for the same question. While there are questions where the answer choices contain more than one correct answer, such questions will always say so and ask you to mark all the correct answers. This is not one of that type of question.
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Re: If 4x + 2 < x^2 + 3x 18 < 0, where x is an integer, what is the valu [#permalink] New post   18 Apr 2024, 21:39
\(4x+2\)<\(x^2+3x−18\)<0­

From \(x^2+3x−18\)<0­ we get that -6<x<3 so we can eliminate A,D,E
Now the options left, when we substitute the values in \(4x+2\)<\(x^2+3x−18\)
For x=-5 we get -18<-8 which is true 
For x=-4 we get -14<-14 which is not true 

Therefore x = -5
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Re: If 4x + 2 < x^2 + 3x 18 < 0, where x is an integer, what is the valu [#permalink]
18 Apr 2024, 21:39
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