# How do you solve 5<2x+7<13?

Jan 7, 2017

See full solution process below

#### Explanation:

While solving this set of inequalities we need to perform each operation to all three parts of the set of inequalities to keep everything balanced.

First, subtract #color(red)(7) from each term in the inequalities:

$5 - \textcolor{red}{7} < 2 x + 7 - \textcolor{red}{7} < 13 - \textcolor{red}{7}$

$- 2 < 2 x + 0 < 6$

$- 2 < 2 x < 6$

Now, we can divide each portion of the inequalities by $\textcolor{red}{2}$ to solve for $x$ while keeping the inequality set balanced:

$\frac{- 2}{\textcolor{red}{2}} < \frac{2 x}{\textcolor{red}{2}} < \frac{6}{\textcolor{red}{2}}$

$- 1 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} < 3$

$- 1 < x < 3$