$$ \begin{aligned} \frac{3x+5}{2x+1} &= \frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ (2x+1)\cdot3 }. \\[1 em](2x+1)\cdot3 \cdot \frac{3x+5}{2x+1} &= (2x+1)\cdot3\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]9x+15 &= 2x+1&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 15 }$ to the right} \\[1 em]9x-2x &= 1-15&& \text{simplify left and right hand side} \\[1 em]7x &= -14&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= -\frac{14}{7}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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