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Which of the following values of x satisfy both inequalities

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Which of the following values of x satisfy both inequalities  [#permalink]

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New post Updated on: 17 Jun 2013, 05:46
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(x —1)(x + 3) > 0
(x +5)(x—4) < 0

Which of the following values of x satisfy both inequalities shown?

I. -6
II. -4
III. 2
IV. 5

A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV

Originally posted by ritumaheshwari02 on 29 Nov 2012, 10:25.
Last edited by Bunuel on 17 Jun 2013, 05:46, edited 2 times in total.
Renamed the topic.
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Re: Which of the following values of x satisfy both inequalities  [#permalink]

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New post 29 Nov 2012, 10:37
1
1
(x —1)(x + 3) > 0
(x +5)(x—4) < 0

Which of the following values of x satisfy both inequalities shown?

I. -6
II. -4
III. 2
IV. 5


A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV

(x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.

Among choices only -4 and 2 satisfy both inequalities.

Answer: C.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html
xy-plane-71492.html
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Re: Which of the following values of x satisfy both inequalities  [#permalink]

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New post 01 Dec 2012, 05:01
Bunuel wrote:
(x —1)(x + 3) > 0
(x +5)(x—4) < 0

Which of the following values of x satisfy both inequalities shown?

I. -6
II. -4
III. 2
IV. 5


A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV

(x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.

Among choices only -4 and 2 satisfy both inequalities.

Answer: C.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html
xy-plane-71492.html


Hi Bunuel,

What is the underlying concept to solve these types of inequalities ? When (x - 1)(x + 3) > 0 , we can assume that either both entities are negative or positive. You seem to have assumed both x-1 and x +3 to be positive. Please do let me know where I'm going wrong in in analysing your solution.

Thanks
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Re: Which of the following values of x satisfy both inequalities  [#permalink]

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New post 01 Dec 2012, 06:06
kheba wrote:
Bunuel wrote:
(x —1)(x + 3) > 0
(x +5)(x—4) < 0

Which of the following values of x satisfy both inequalities shown?

I. -6
II. -4
III. 2
IV. 5


A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV

(x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.

Among choices only -4 and 2 satisfy both inequalities.

Answer: C.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html
xy-plane-71492.html


Hi Bunuel,

What is the underlying concept to solve these types of inequalities ? When (x - 1)(x + 3) > 0 , we can assume that either both entities are negative or positive. You seem to have assumed both x-1 and x +3 to be positive. Please do let me know where I'm going wrong in in analysing your solution.

Thanks


Concept is explained in the topics given in my previous post.
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Re: Which of the following values of x satisfy both inequalities  [#permalink]

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New post 19 May 2016, 09:29
Backsolving was quick :)

C satisfies the equation
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Re: Which of the following values of x satisfy both inequalities  [#permalink]

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New post 24 Dec 2018, 11:38
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Re: Which of the following values of x satisfy both inequalities   [#permalink] 24 Dec 2018, 11:38
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