# How do you solve 13< 2x - 1< 17?

Oct 9, 2016

$7 < x < 9$

#### Explanation:

Solve this as two separate inequalities first, and then combine them at the end.

$13 < 2 x - 1 < 17$ can be split into:

$\textcolor{red}{13 < 2 x - 1} \text{ and } \textcolor{b l u e}{2 x - 1 < 17}$

$\textcolor{red}{13 + 1 < 2 x} \text{ and } \textcolor{b l u e}{2 x < 17 + 1}$

$\textcolor{red}{14 < 2 x} \text{ and } \textcolor{b l u e}{2 x < 18}$

$\textcolor{red}{7 < x} \text{ and "color(blue)(x< 9)" } \leftarrow$ the x is the same

$\textcolor{w h i t e}{\times \times x} 7 < x < 9$