# How do you solve the compound inequality 4<2y-2<10?

May 11, 2018

$3 < y < 6$

#### Explanation:

$\text{isolate "2y" by adding 2 to each of the 3 intervals}$

$4 \textcolor{red}{+ 2} < 2 y \cancel{- 2} \cancel{\textcolor{red}{+ 2}} < 10 \textcolor{red}{+ 2}$

$\Rightarrow 6 < 2 y < 12$

$\text{divide each interval by 2}$

$\Rightarrow 3 < y < 6$

$y \in \left(3 , 6\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$