# If 4-x^2>=0 isn't x<=+-2? I don't understand how -2<=x<=2 is a result.

## $4 - {x}^{2} \ge 0$ isn't $x \le \pm 2$? I don't understand how $- 2 \le x \le 2$ is the result?

Dec 28, 2017

#### Explanation:

As $4 - {x}^{2} \ge 0$, we have $\left(2 - x\right) \left(2 + x\right) \ge 0$

This means product of $\left(2 - x\right)$ and $\left(2 + x\right)$ is positive. Hence either both are positive or both are negative.

If both are positive we have $2 - x \ge 0$ i.e. $x \le 2$ and $2 + x \ge 0$ i.e. $x \ge - 2$. Hence we have $- 2 \le x \le 2$.

If both are negative we have $2 - x \le 0$ i.e. $x \ge 2$ and $2 + x \le 0$ i.e. $x \le - 2$. We cannot have the two together.

Hence answer is $- 2 \le x \le 2$