$$ \begin{aligned} \frac{2x-5}{3} &= x+1&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{2x-5}{3} &= 3x+3\cdot1&& \text{cancel out the denominators} \\[1 em]2x-5 &= 3x+3&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -5 }$ to the right} \\[1 em]2x-3x &= 3+5&& \text{simplify left and right hand side} \\[1 em]-x &= 8&& \text{switch signs on both sides} \\[1 em]x &= -8&& \\[1 em] \end{aligned} $$

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