# How do you solve 13x-11<=7x+37?

Feb 11, 2017

See the entire solution process below:

#### Explanation:

First, add $\textcolor{red}{11}$ and subtract $\textcolor{b l u e}{7 x}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$13 x - 11 + \textcolor{red}{11} - \textcolor{b l u e}{7 x} \le 7 x + 37 + \textcolor{red}{11} - \textcolor{b l u e}{7 x}$

$13 x - \textcolor{b l u e}{7 x} - 11 + \textcolor{red}{11} \le 7 x - \textcolor{b l u e}{7 x} + 37 + \textcolor{red}{11}$

$6 x - 0 \le 0 + 48$

$6 x \le 48$

Now, divide each side of the inequality by $\textcolor{red}{6}$ to solve for $x$ while keeping the inequality balanced:

$\frac{6 x}{\textcolor{red}{6}} \le \frac{48}{\textcolor{red}{6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} x}{\cancel{\textcolor{red}{6}}} \le 8$

$x \le 8$