If 4x + 2

Question

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

nick1816 · Answer

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

Kinshook · Answer

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

yashikaaggarwal · Answer

4x+2 4x+2 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 4(-5)+2<(-5)^2+3(-5)-18<0 => -20+2<25-15-18<0 => -18<-8<0 (Satisfying) C. X = -4 => 4x+2 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 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 4(7)+2<(7)^2+3(7)-18<0 => 28+2<49+21-18<0 => 30<52>0 (not satisfying) Answer is B Posted from my mobile device

Superman249 · Answer

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

ScottTargetTestPrep · Answer

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

Lipun · Answer

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

ScottTargetTestPrep · Answer

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.

sset92 · Answer

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

bumpbot · Answer

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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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