First slide

Introduction to real valued functions

Question

Number of integral values of x satisfying the inequality $\frac{x^{2} + 6 x - 7}{| x + 2 | | x + 3 |} < 0$ is

Moderate

A

5
B

6
C

7
D

8

Solution

We have $\frac{x^{2} + 6 x - 7}{| x + 2 | | x + 3 |} < 0$
Clearly, $x \neq - 2, - 3$
Now, $x^{2} + 6 x - 7 < 0$
$\begin{array}{ll} \Rightarrow (x + 7) (x - 1) < 0 \\ \Rightarrow x \in (- 7, 1) - {- 3, - 2} \end{array}$
So, integers are ${- 6, - 5, - 4, - 1, 0}$

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