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

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