# How do you solve 1/3x -1/9<1/6?

Jan 25, 2017

See the entire solution process below:

#### Explanation:

First, multiple the entire inequality by $\textcolor{red}{18}$ (the lowest common denominator of the fractions) to eliminate the fractions and keep the inequality balanced:

$\textcolor{red}{18} \left(\frac{1}{3} x - \frac{1}{9}\right) < \textcolor{red}{18} \times \frac{1}{6}$

$\left(\textcolor{red}{18} \times \frac{1}{3} x\right) - \left(\textcolor{red}{18} \times \frac{1}{9}\right) < \frac{18}{6}$

$\frac{18}{3} x - \frac{18}{9} < \frac{18}{6}$

$6 x - 2 < 3$

Next, add $\textcolor{red}{2}$ to each side of the inequality to isolate the $x$ term while keeping the inequality balanced.

$6 x - 2 + \textcolor{red}{2} < 3 + \textcolor{red}{2}$

$6 x - 0 < 5$

$6 x < 5$

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

$\frac{6 x}{\textcolor{red}{6}} < \frac{5}{\textcolor{red}{6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} x}{\cancel{\textcolor{red}{6}}} < \frac{5}{6}$

$x < \frac{5}{6}$