# How do you solve 1/2x-9<2x?

Jan 14, 2017

See entire solution process below:

#### Explanation:

First, multiply each side of the inequality by $\textcolor{red}{2}$ to eliminate the fraction and keep the inequality balanced:

$\textcolor{red}{2} \times \left(\frac{1}{2} x - 9\right) < \textcolor{red}{2} \times 2 x$

$\left(\textcolor{red}{2} \times \frac{1}{2} x\right) - \left(\textcolor{red}{2} \times 9\right) < 4 x$

$x - 18 < 4 x$

Next, we subtract $\textcolor{red}{x}$ from each side of the equation to isolate the $x$ terms on one side of the inequality and the constants on the other side of the inequality while keeping the inequality balanced:

$x - \textcolor{red}{x} - 18 < 4 x - \textcolor{red}{x}$

$0 - 18 < \left(4 - 1\right) x$

$- 18 < 3 x$

Now we can divide each side of the inequality by $\textcolor{red}{3}$ to solve for $x$ and keep the inequality balanced:

$- \frac{18}{\textcolor{red}{3}} < \frac{3 x}{\textcolor{red}{3}}$

$- 6 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}}$

$- 6 < x$

Then, we can reverse or "flip" the inequality to solve in terms of $x$:

$x > - 6$