$$ \begin{aligned} \frac{1}{4}(x+2)+5 &= -x&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{4}(x+2)+4\cdot5 &= -4x&& \text{cancel out the denominators} \\[1 em]x+2+20 &= -4x&& \text{simplify left side} \\[1 em]x+22 &= -4x&& \text{move the $ \color{blue}{ -4x } $ to the left side and $ \color{blue}{ 22 }$ to the right} \\[1 em]x+4x &= -22&& \text{simplify left side} \\[1 em]5x &= -22&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{22}{5}&& \\[1 em] \end{aligned} $$

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