How many of the numbers $-5,-4,-3,-2,-1,0$, $1,2,3$ satisfy the inequality $-3 x^{2}<-14$?
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
The correct option is (d).

If $-3 x^{2}14$, or $x^{2}>\frac{1}{3} 14=4 \frac{2}{3}$. Since we are only looking at integer values of $x$, then $x^{2}$ is also an integer. Given that $x^{2}>4 \frac{2}{3}$, we conclude that $x^{2}$ is at least 5. Among the numbers $-5,-4,-3,-2,-1,0,1,2,3$ only four, namely, $-5,-4,-3$ and 3 satisfy $x^{2} \geq 5$.