College Algebra, Chapter 1, 1.1, Section 1.1, Problem 36

The equation $\displaystyle \frac{2}{3} x - \frac{1}{4} = \frac{1}{6} x - \frac{1}{9}$ is either linear or equivalent to a linear equation. Solve the equation

$\begin{equation} \begin{aligned} \frac{2}{3} x - \frac{1}{4} &= \frac{1}{6} x - \frac{1}{9} && \text{Combine like terms}\\ \\ \frac{2x}{3} - \frac{x}{6} &= \frac{1}{4} - \frac{1}{9} && \text{Get the LCD}\\ \\ \frac{4x-x}{6} &= \frac{9-4}{36} && \text{Simplify}\\ \\ \frac{3x}{6} &= \frac{5}{36} && \text{Multiply both sides by } \frac{6}{3}\\ \\ \frac{\cancel{6}}{\cancel{3}} & \left[ \frac{\cancel{3}x}{\cancel{6}} = \frac{5}{36} \right] \frac{6}{3} && \text{Simplify}\\ \\ x &= \frac{5}{(6)(3)} && \text{Simplify}\\ \\ x &= \frac{5}{18} \end{aligned} \end{equation}$