# How do you solve and write the following in interval notation: -3 ≤ (x − 4) / 2 <4?

Jul 14, 2016

$x$ will be in the interval $\left[- 2 , 12\right)$.

#### Explanation:

When manipulating an inequality, we can treat it as a three part equation. Whenever we alter one part, we do the same to the other two. This allows us to manipulate the equation like so:
-3 ≤ (x − 4) / 2 < 4
-6 ≤ x − 4 < 8
-2 ≤ x < 12

So the final answer is that $x$ will be in the interval $\left[- 2 , 12\right)$.

Jul 14, 2016

x in[-2,12[

#### Explanation:

First, you can multiply all terms by 2:

$- 6 \le x - 4 < 8$

and then you can add 4 to all terms:

$- 2 \le x < 12$