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What is the scope of x such that (x-1)(x+4)

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What is the scope of x such that (x-1)(x+4)  [#permalink]

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New post 14 Aug 2018, 19:26
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A
B
C
D
E

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  45% (medium)

Question Stats:

63% (02:07) correct 37% (02:27) wrong based on 55 sessions

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What is the scope of x such that \(\frac{(x-1)(x+4)}{(x+2)} <x\)?

A. \(-2<x<4\)
B. \(-4<x<4\)
C. \(-2<x<2\)
D. \(-2<x\)
E. \(0<x<3\)
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Re: What is the scope of x such that (x-1)(x+4)  [#permalink]

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New post 14 Aug 2018, 19:53
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ammuseeru wrote:
What is the scope of x such that \(\frac{(x-1)(x+4)}{(x+2)} <x\)?

A. \(-2<x<4\)
B. \(-4<x<4\)
C. \(-2<x<2\)
D. \(-2<x\)
E. \(0<x<3\)



\(\frac{(x-1)(x+4)}{(x+2)} <x.........\frac{x^2+3x-4}{x+2}\)-x<0
\(\frac{x^2+3x-4-x^2-2x}{x+2}<0.............\frac{x-4}{x+2}<0\)..
So two cases...
1) x-4>0, then x+2<0........x<-2 and x>4.... No overlap in two regions
2) x-4<0, then x+2>0.......-2<x<4.....
So A

Also use choices..
Check for X at -3, 3 and you will be able to get our answer..
1) x=3
\(\frac{(x-1)(x+4)}{(x+2)} <x........

\frac{(3-1)(3+4)}{3+2}<3........2*7/5<3.......14<15\) yes
Eliminate all those which do not contain 3, so C and E are out.

2) x=-3
\(\frac{(x-1)(x+4)}{(x+2)} <x....
..\frac{(-3-1)(-3+4)}{-3+2}<-3........(-4)*1/(-1)<-3......4<-3\).. No
So eliminate those containing -3, so B out

3) remaining A and D
Look for x = 5..
(5-1)(5+4)/(5+2)<5......4*20/7<5.....80<35.....no
So eliminate D

A
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Re: What is the scope of x such that (x-1)(x+4)  [#permalink]

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New post 14 Aug 2018, 20:05
ammuseeru wrote:
What is the scope of x such that \(\frac{(x-1)(x+4)}{(x+2)} <x\)?

A. \(-2<x<4\)
B. \(-4<x<4\)
C. \(-2<x<2\)
D. \(-2<x\)
E. \(0<x<3\)


Another easy way is to consider the oprions.
Put x=0, LHS<RHS TRUE
Option E is out.

Put x=3 LHS<RHS TRUE
Option C is out.

Put x=-3 LHS>RHS FALSE
Option B is out.

Put x=5 LHS>RHS FALSE
Option D is out.

Hence Option A is correct.

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Re: What is the scope of x such that (x-1)(x+4)  [#permalink]

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New post 14 Aug 2018, 22:47
ammuseeru wrote:
What is the scope of x such that \(\frac{(x-1)(x+4)}{(x+2)} <x\)?

A. \(-2<x<4\)
B. \(-4<x<4\)
C. \(-2<x<2\)
D. \(-2<x\)
E. \(0<x<3\)

\(\frac{(x-1)(x+4)}{(x+2)} <x\)

Or, \(x^2+3x−4 < x^2 + 2x\)

Or, \(x < 4\)

Now check using options given, Answer must be (A), as shown in the above posts....
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Re: What is the scope of x such that (x-1)(x+4)  [#permalink]

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New post 14 Aug 2018, 22:58
ammuseeru wrote:
What is the scope of x such that \(\frac{(x-1)(x+4)}{(x+2)} <x\)?

A. \(-2<x<4\)
B. \(-4<x<4\)
C. \(-2<x<2\)
D. \(-2<x\)
E. \(0<x<3\)


\(\frac{(x-1)(x+4)}{(x+2)} <x\)

Solving for x =>

\((x^2 - x + 4x - 4) < (x^2 + 2x)\)

(3x - 2x) < 4

Therefore, x < 4

Now if we look at the options, we find two options namely A and B having,

x < 4

On comparing its range start parameters, we get 3 as the eliminator between both

Substituting x = 3 in \(\frac{(x-1)(x+4)}{(x+2)} <x\)

\(\frac{(-4) * (1)}{(-1)} < (-3)\)

On solving we get
LHS = 4
RHS = -3

as LHS is not less than RHS.

Answer is Option A
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Re: What is the scope of x such that (x-1)(x+4)  [#permalink]

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New post 15 Aug 2018, 09:34
1
ammuseeru wrote:
What is the scope of x such that \(\frac{(x-1)(x+4)}{(x+2)} <x\)?

A. \(-2<x<4\)
B. \(-4<x<4\)
C. \(-2<x<2\)
D. \(-2<x\)
E. \(0<x<3\)


Given, \(\frac{(x-1)(x+4)}{(x+2)} <x\)
Or, \(\frac{\left(x-1\right)\left(x+4\right)}{x+2}-x<0\)
Or, \(\frac{\left(x-1\right)\left(x+4\right)-x\left(x+2\right)}{x+2}<0\)
Or, \(\frac{x-4}{x+2}<0\)
Or, \(-2<x<4\)

Ans. (A)
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Re: What is the scope of x such that (x-1)(x+4)   [#permalink] 15 Aug 2018, 09:34
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