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The number of elements in the set ${x \in \mathbb{R} : (|x| - 3)|x + 4| = 6}$ is equal to
(1) 3
(2) 2
(3) 4
(4) 1
$x \neq -4$
$(|x| - 3)(|x + 4|) = 6$
$\Rightarrow |x| - 3 = \frac{6}{|x+4|}$
By plotting $y = |x| - 3$ and $y = \frac{6}{|x+4|}$:
No. of solutions $= 2$
BETA
