Let $S=\left\{x\in[-6,3]-\{-2,2\}:\dfrac{|x+3|-1}{|x|-2}\ge 0\right\}$ and $T=\{x\in\mathbb{Z}:x^2-7|x|+9\le 0\}$. Then the number of elements in $S\cap T$ is
Step-by-Step Solution
Key Concept: Find S by case analysis on x, find T by solving quadratic in |x|
T = {-5,-4,-3,3,4,5} (integers with $|x|$ between roots). $S\cap T$ gives 3 elements.
Correct Answer: 4