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# What is the scope of x such that (x - 1)(x + 4)/(x + 2) < x ?

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Math Expert
Joined: 02 Sep 2009
Posts: 60727
What is the scope of x such that (x - 1)(x + 4)/(x + 2) < x ?  [#permalink]

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25 Nov 2019, 01:31
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Difficulty:

65% (hard)

Question Stats:

58% (02:18) correct 42% (02:02) wrong based on 36 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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Joined: 19 Oct 2018
Posts: 1297
Location: India
Re: What is the scope of x such that (x - 1)(x + 4)/(x + 2) < x ?  [#permalink]

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25 Nov 2019, 04:22
$$\frac{(x-1)(x+4)}{(x+2)} <x$$

$$\frac{(x-1)(x+4)}{(x+2)} -x<0$$

$$\frac{x-4}{x+2}<0$$

-2<x<4

Bunuel 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. $$0<x<3$$

Are You Up For the Challenge: 700 Level Questions
VP
Joined: 24 Nov 2016
Posts: 1139
Location: United States
What is the scope of x such that (x - 1)(x + 4)/(x + 2) < x ?  [#permalink]

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25 Nov 2019, 08:59
Bunuel 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. $$0<x<3$$

$$\frac{(x-1)(x+4)}{(x+2)}<x…\frac{(x-1)(x+4)}{x+2}-x<0…\frac{(x-1)(x+4)-x(x+2)}{x+2}<0$$

$$\frac{(x-1)(x+4)-[x^2+2x]}{x+2}<0…\frac{x^2+4x-x-4-x^2-2x}{x+2}<0…\frac{x-4}{x+2}<0$$

$$\frac{x-4}{x+2}<0…(less.than=inside.rng;x≠-2=divby:0)…-2<x<4$$

Ans (A)
What is the scope of x such that (x - 1)(x + 4)/(x + 2) < x ?   [#permalink] 25 Nov 2019, 08:59
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