College Algebra, Chapter 1, 1.1, Section 1.1, Problem 28

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

$\begin{equation} \begin{aligned} 2x - \frac{x}{2} + \frac{x+1}{4} &= 6x && \text{Get the LCD of the left side}\\ \\ \frac{8x - 2x + x + 1}{4} &= 6x && \text{Simplify}\\ \\ \frac{7x+1}{4} &= 6x && \text{Group}\\ \\ \frac{7x}{4} + \frac{1}{4} &= 6x && \text{Combine like terms}\\ \\ \frac{7x}{4} - 6x &= \frac{-1}{4} && \text{Get the LCD of the left side}\\ \\ \frac{7x-24x}{4} &= \frac{-1}{4} && \text{Simplify}\\ \\ \frac{-17x}{4} &= \frac{-1}{4} && \text{Multiply both sides by -4}\\ \\ -\cancel{4}& \left[ \frac{-17x}{\cancel{4}}= \frac{-1}{4} \right] - \cancel{4} && \text{Simplify}\\ \\ 17x &= 1 && \text{Divide both sides by 17}\\ \\ \frac{\cancel{17}x}{\cancel{17}} &= \frac{1}{17} && \text{Simplifty}\\ \\ x &= \frac{1}{17} \end{aligned} \end{equation}$