How many numbers from the set $\{-5,-4,-3,-2,-1,0,1,2,3\}$ satisfy the inequality $-3 x^{2}<-14$ ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Solution 1

If $-3 x^{2}14$ or $x^{2}>\frac{14}{3}=4 \frac{2}{3}$.

Since we are only looking at $x$ being a whole number, then $x^{2}$ is also a whole number. Since $x^{2}$ is a whole number and $x^{2}$ is greater than $4 \frac{2}{3}$, then $x^{2}$ must be at least 5 .

Of the numbers in the set, the ones which satisfy this condition are $-5,-4,-3$, and 3 .

## Solution 2

For each number in the set, we substitute the number for $x$ and calculate $-3 x^{2}$ :

| $x$ | $-3 x^{2}$ |
| :---: | :---: |
| -5 | -75 |
| -4 | -48 |
| -3 | -27 |
| -2 | -12 |
| -1 | -3 |
| 0 | -3 |
| 0 | -12 |

As before, the four numbers $-5,-4,-3$, and 3 satisfy the inequality.

ANSWER: (D)