$$ \begin{aligned} \frac{1}{4}(x+5)-\frac{1}{3}-(x+5) &= -7&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{1}{4}(x+5)-12\cdot\frac{1}{3}-12(x+5) &= 12\cdot(-7)&& \text{cancel out the denominators} \\[1 em]3x+15-4-(12x+60) &= -84&& \text{simplify left side} \\[1 em]3x+11-(12x+60) &= -84&& \\[1 em]3x+11-12x-60 &= -84&& \\[1 em]-9x-49 &= -84&& \text{ move -49 to the right } \\[1 em]-9x &= -84+49&& \\[1 em]-9x &= -35&& \text{ divide both sides by $ -9 $ } \\[1 em]x &= \frac{-35}{-9}&& \\[1 em]x &= \frac{35}{9}&& \\[1 em] \end{aligned} $$

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