$$x+3 = \frac{5}{3}x-1$$

$$ \begin{aligned} x+3 &= \frac{5}{3}x-1&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3x+3\cdot3 &= 3 \cdot \frac{5}{3}x-3\cdot1&& \text{cancel out the denominators} \\[1 em]3x+9 &= 5x-3&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]3x-5x &= -3-9&& \text{simplify left and right hand side} \\[1 em]-2x &= -12&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-12}{-2}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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