# CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

###### CAT Questions | Algebra | Properties of Inequalities CAT Questions

The question is for finding the solution of a inequality. We need to solve the inequality which is in the form of fraction. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.

Question 17: Solve :$$frac{$x – 4$ (x+3)}{(x + 4) ( x +5)}$ > 0? 1. x ∊$-∞,-1] ∪ [√3, 3)
2. x ∊ (-∞,-3] ∪ [√3, ∞)
3. x ∊ (-4,-3) ∪ (4, ∞)
4. x ∊ (-8,-3] ∪ [2, ∞)

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##### Method of solving this CAT Question from Algebra - Inequalities : Solve for x in the traditonal approach!!

$$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 (-∞,-5) ∪ (4, ∞)

The question is "Solve :$$frac{$x – 4$ (x + 3)}{(x + 4) ( x + 5)}$ > 0?" ##### Hence the answer is "x ∊$-∞,-1] ∪ [√3, 3)"

Choice A is the correct answer.

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