$$ \begin{aligned} 3 \cdot \frac{2x-5}{4} &= 2 \cdot \frac{2x+1}{3}+1&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot3 \cdot \frac{2x-5}{4} &= 12\cdot2 \cdot \frac{2x+1}{3}+12\cdot1&& \text{cancel out the denominators} \\[1 em]18x-45 &= 16x+8+12&& \text{simplify right side} \\[1 em]18x-45 &= 16x+20&& \text{move the $ \color{blue}{ 16x } $ to the left side and $ \color{blue}{ -45 }$ to the right} \\[1 em]18x-16x &= 20+45&& \text{simplify left and right hand side} \\[1 em]2x &= 65&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{65}{2}&& \\[1 em] \end{aligned} $$

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