First slide

Introduction to sets

Question

$Which of the following is not the solution of \frac{| x + 3 | + x}{x + 2} >1?$

Moderate

A

$(- 5, - 2)$
B

$(- 1, \infty)$
C

$(- 5, - 1)$
D

None of these

Solution

$We have \frac{| x + 3 | + x}{x + 2} > 1$
$Clearly, LHS of this inequation is meaningful for x \neq - 2 .$
$\begin{aligned} Now \frac{| x + 3 | + x}{x + 2} - 1 > 0 \\ \Rightarrow \frac{| x + 3 | - 2}{x + 2} > 0 \end{aligned}$
$If | x + 3 | - 2 = 0 \Rightarrow x + 3 = \pm 2 \Rightarrow x = - 5, - 1$
$Hence, the sign scheme of the expression \frac{| x + 3 | - 2}{x + 2} is as follows:$

$From the above sign scheme x \in (- 5, - 2) \cup (- 1, \infty) .$

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