# How do you solve and write the following in interval notation:  -8< -2x – 1 ≤ -5?

##### 1 Answer
Jul 16, 2018

$\left[2 , \frac{7}{2}\right)$

#### Explanation:

Remember, we want only an $x$ in the middle on the inequality, so whatever we do, we must to it to all three parts.

We can start by adding $1$ to all three parts to get

$- 7 < - 2 x \le - 4$

To get just an $x$ in the middle, we can divide all parts by $- 2$. Recall that dividing or multiplying by a negative flips the signs. We get

$\frac{7}{2} > x \ge 2$, which is the same as $2 \le x < \frac{7}{2}$. In interval notation, we can write this as

$\left[2 , \frac{7}{2}\right)$

Note that the bracket means we include the bound, and the parenthesis means we don't include it.

This is the same as saying all values between $x = 2$ and $x = \frac{7}{2}$, including $2$ and not including $\frac{7}{2}$.

Hope this helps!