$$ \begin{aligned} \frac{x}{3}+2x+\frac{4}{4} &= x-\frac{1}{6}-3-2\frac{x}{2}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x}{3}+12\cdot2x+12\cdot\frac{4}{4} &= 12x-12\cdot\frac{1}{6}-12\cdot3-12\cdot2\frac{x}{2}&& \text{cancel out the denominators} \\[1 em]4x+24x+12 &= 12x-2-36-12x&& \text{simplify left and right hand side} \\[1 em]28x+12 &= 12x-2-36-12x&& \\[1 em]28x+12 &= -38&& \text{ move 12 to the right } \\[1 em]28x &= -38-12&& \\[1 em]28x &= -50&& \text{ divide both sides by $ 28 $ } \\[1 em]x &= -\frac{50}{28}&& \\[1 em]x &= -\frac{25}{14}&& \\[1 em] \end{aligned} $$

This page was created using