$$\frac{x}{4}+13 = 2x-22$$

$$ \begin{aligned} \frac{x}{4}+13 &= 2x-22&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{x}{4}+4\cdot13 &= 4\cdot2x-4\cdot22&& \text{cancel out the denominators} \\[1 em]x+52 &= 8x-88&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 52 }$ to the right} \\[1 em]x-8x &= -88-52&& \text{simplify left and right hand side} \\[1 em]-7x &= -140&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= \frac{-140}{-7}&& \\[1 em]x &= 20&& \\[1 em] \end{aligned} $$

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