The number of elements in the set {x in R : ( | vedclass

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(B) To find the number of elements in the set,we solve the equation $(|x|-3)|x+4|=6$.Let $f(x) = |x|-3$ and $g(x) = \frac{6}{|x+4|}$.We look for the n

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$2$

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(B) To find the number of elements in the set,we solve the equation $(|x|-3)|x+4|=6$.Let $f(x) = |x|-3$ and $g(x) = \frac{6}{|x+4|}$.We look for the number of intersection points of the graphs of $y = |x|-3$ and $y = \frac{6}{|x+4|}$.The graph of $y = |x|-3$ is a $V$-shaped curve with its vertex at $(0, -3)$ and x-intercepts at $x = 3$ and $x = -3$.The graph of $y = \frac{6}{|x+4|}$ is a hyperbola-like curve with a vertical asymptote at $x = -4$ and it is always positive.By observing the graphs,the curve $y = |x|-3$ intersects $y = \frac{6}{|x+4|}$ at two distinct points: one in the interval $(3, \infty)$ and one in the interval $(-\infty, -4)$.Therefore,the number of elements in the set is $2$.

The number of elements in the set $\{x \in R : (|x|-3)|x+4|=6\}$ is equal to

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