$$2 \cdot \frac{x}{3}+5 = 11 \cdot \frac{x}{15}+14$$

$$ \begin{aligned} 2 \cdot \frac{x}{3}+5 &= 11 \cdot \frac{x}{15}+14&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15\cdot2 \cdot \frac{x}{3}+15\cdot5 &= 15\cdot11 \cdot \frac{x}{15}+15\cdot14&& \text{cancel out the denominators} \\[1 em]10x+75 &= 11x+210&& \text{move the $ \color{blue}{ 11x } $ to the left side and $ \color{blue}{ 75 }$ to the right} \\[1 em]10x-11x &= 210-75&& \text{simplify left and right hand side} \\[1 em]-x &= 135&& \text{switch signs on both sides} \\[1 em]x &= -135&& \\[1 em] \end{aligned} $$

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