# The number of elements in the set

Question:

The number of elements in the set

$\{x \in \mathbb{R}:(|x|-3)|x+4|=6\}$ is equal to

1. (1) 3

2. (2) 2

3. (3) 4

4. (4) 1

Correct Option: , 2

Solution:

$x \neq-4$

$(|x|-3)(|x+4|)=6$

$\Rightarrow \quad|x|-3=\frac{6}{|x+4|}$

No. of solutions $=2$