$$\frac{2}{3}(5x+7) = 8x$$

$$ \begin{aligned} \frac{2}{3}(5x+7) &= 8x&& \text{simplify left side} \\[1 em]\frac{10x+14}{3} &= 8x&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{10x+14}{3} &= 3\cdot8x&& \text{cancel out the denominators} \\[1 em]10x+14 &= 24x&& \text{move the $ \color{blue}{ 24x } $ to the left side and $ \color{blue}{ 14 }$ to the right} \\[1 em]10x-24x &= -14&& \text{simplify left side} \\[1 em]-14x &= -14&& \text{ divide both sides by $ -14 $ } \\[1 em]x &= \frac{-14}{-14}&& \\[1 em]x &= 1&& \\[1 em] \end{aligned} $$

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