$$ \begin{aligned} 3x+2(x-3) &= \frac{113}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot3x+2\cdot2(x-3) &= 2\cdot\frac{113}{2}&& \text{cancel out the denominators} \\[1 em]6x+4x-12 &= 113&& \text{simplify left side} \\[1 em]10x-12 &= 113&& \text{ move -12 to the right } \\[1 em]10x &= 113+12&& \\[1 em]10x &= 125&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{125}{10}&& \\[1 em]x &= \frac{25}{2}&& \\[1 em] \end{aligned} $$

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