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

Question

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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nick1816 · Answer

\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

exc4libur · Answer

\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}<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)

Su1206 · Answer

Bunuel  please explain how the final step is done. cant understand how x-4/x+2 is translated to -2<x<4

Bunuel · Answer

We have: \frac{x-4}{x+2}<0 The transition points are x = -2 and x = 4 (these are the values of x for which the numerator or denominator equals 0). This gives us three ranges: x < -2 -2 < x < 4 x > 4 Next, test an extreme value for x: if x is a large enough number, say 10, then both the numerator and denominator will be positive, resulting in a positive value for the whole expression. Therefore, when x > 4, the expression is positive. Now, here’s the trick: since the expression is positive in the 3rd range, it will be negative in the 2nd range and positive again in the 1st range, following the pattern: +, -, +. Thus, the expression is negative for -2 < x < 4 . Inequalities Theory: Inequalities Made Easy! Inequalities: Tips and hints Arithmetic with Inequalities Wavy Line Method Application - Complex Algebraic Inequalities Solving Quadratic Inequalities: Graphic Approach Inequalities - Quadratic Inequalities Graphic approach to problems with inequalities Inequalities trick INEQUATIONS(Inequalities) Part 1 INEQUATIONS(Inequalities) Part 2 Questions: Inequality and absolute value questions from my collection DS Questions PS Questions For more check Ultimate GMAT Quantitative Megathread Hope it helps.

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

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