$$ \begin{aligned} \frac{11}{2} &= \frac{3}{2}x+\frac{3}{5}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot\frac{11}{2} &= 10 \cdot \frac{3}{2}x+10\cdot\frac{3}{5}&& \text{cancel out the denominators} \\[1 em]55 &= 15x+6&& \text{ swap the left and right side of the equation } \\[1 em]15x+6 &= 55&& \text{ move 6 to the right } \\[1 em]15x &= 55-6&& \\[1 em]15x &= 49&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{49}{15}&& \\[1 em] \end{aligned} $$

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