# How do you express intervals as inequalities such as [-2,9]?

Feb 20, 2017

$\left[- 2 , 9\right]$ is written as the inequality $- 2 \le x \le 9$

#### Explanation:

The expression $\left[- 2 , 9\right]$ in interval form means that

the concerned variable, say $x$ has a lower limit of $- 2$ and including $- 2$, as we have square brackets but had we parentheses i.e. '(', this means that $- 2$ is not included.

In other words $x \ge - 2$ as value of $x$ is not less than $- 2$.

Further, as the interval has an upper limit of $9$, again including $9$, as we have square brackets but had we parentheses i.e. '(', this means that $9$ is not included.

In other words $x \le 9$ as value of $x$ is not greater than $- 2$.

The two limits can then be combined as $- 2 \le x \le 9$

Note that had it be $\left(- 2 , 9\right)$,

the result would have been $- 2 < x < 9$.

$\left(- 2 , 9\right]$ as $- 2 < x \le 9$

and $\left[- 2 , 9\right)$ as $- 2 \le x < 9$