# CAT Practice : Inequalities

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Solve for x in the traditonal approach!!

## Properties of Inequalities

Q.17:Solve :$\frac{(x – 4) (x+3)}{(x + 4) ( x +5)} > 0$
1. $(-\infty,-5) \cup (4, \infty)$
2. $(-\infty,-3] \cup [3, \infty)$
3. $(-\infty,-5] \cup [1, \infty)$
4. $(-\infty,-1] \cup [2, \infty)$

Choice A. $(-\infty,-5) \cup (4, \infty)$

## Detailed Solution

$\frac{(x – 4) (x+3)}{(x + 4) ( x +5)} > 0$
Consider this as $\frac{a}{b}$ > 0
Here both a > 0 & b > 0 or a < 0 & b < 0

Case 1: (x – 4) (x + 3) > 0 & (x + 4) ( x +5) > 0
x > 4 , x > -3, x > -4 , x > -5
Combining all we get x > 4

Case 2: (x – 4) (x + 3) < 0 & (x + 4) ( x +5) < 0
x < 4, x < -3, x < -4, x < -5
Combining all x < -5
Hence range is $(-\infty,-5) \cup (4, \infty)$

Correct Answer: $(-\infty,-5) \cup (4, \infty)$

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## More questions from Inequalities

Inequalities are crucial to understand many topics that are tested in the CAT. Having a good foundation in this subject will make us tackling questions in Coordinate Geometry, Functions, and most importantly in Algebra much more comfortable.