$$ \begin{aligned} 3+\frac{2x}{8}-\frac{4x+12}{8} &= 1-5 \cdot \frac{x+3}{8}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8\cdot3+8 \cdot \frac{2x}{8}-8\frac{4x+12}{8} &= 8\cdot1-8\cdot5 \cdot \frac{x+3}{8}&& \text{cancel out the denominators} \\[1 em]24+2x-(4x+12) &= 8-(5x+15)&& \text{simplify left and right hand side} \\[1 em]24+2x-4x-12 &= 8-5x-15&& \\[1 em]-2x+12 &= -5x-7&& \text{move the $ \color{blue}{ -5x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]-2x+5x &= -7-12&& \text{simplify left and right hand side} \\[1 em]3x &= -19&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{19}{3}&& \\[1 em] \end{aligned} $$

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