# How do you solve -33<=-7n-12<-26?

Sep 12, 2016

$2 < n \le 3$.

$\text{Writing in the Interval Form, } n \in \left(2 , 3\right]$.

#### Explanation:

$- 33 \le - 7 n - 12 < - 26$.

Adding $12$ throughout,

$- 33 + 12 \le - 7 n - 12 + 12 < - 26 + 12$

$\therefore - 21 \le - 7 n < - 14$.

Now, to separate $n$, we have to divide the inequality by $- 7$, and,

as $- 7$ is a $- v e$ number, the inequality has to be reversed. So,

$- \frac{21}{-} 7 \ge \frac{- 7 n}{-} 7 > - \frac{14}{-} 7 ,$ i.e.,

$3 \ge n > 2$, or what is the same as,

$2 < n \le 3$.

$\text{Writing in the Interval Form, } n \in \left(2 , 3\right]$.