\[\begin{array}{rl}\frac{2}{3}t-2=\frac{3}{2}t+\frac{1}{6}&\text{Multiply each term by the LCD}(2,3,6)=6 \\ \color{blue}{6}\color{black}{}\cdot\frac{2}{3}t-\color{blue}{6}\color{black}{}\cdot 2=\color...\[\begin{array}{rl}\frac{2}{3}t-2=\frac{3}{2}t+\frac{1}{6}&\text{Multiply each term by the LCD}(2,3,6)=6 \\ \color{blue}{6}\color{black}{}\cdot\frac{2}{3}t-\color{blue}{6}\color{black}{}\cdot 2=\color{blue}{6}\color{black}{}\cdot\frac{3}{2}t+\color{blue}{6}\color{black}{}\cdot\frac{1}{6}&\text{Simplify} \\ \frac{12}{3}t-12=\frac{18}{2}t+\frac{6}{6}&\text{Reduce the fractions} \\ 4t-12=9t+1&\text{Isolate the variable term by adding the opposite of }9t \\ &\text{to each side} \\ 4t-12+\color{blue…
