$$\frac{40}{x}+1 = \frac{15}{2}$$

$$ \begin{aligned} \frac{40}{x}+1 &= \frac{15}{2}&& \text{multiply ALL terms by } \color{blue}{ x\cdot2 }. \\[1 em]x\cdot2\cdot\frac{40}{x}+x\cdot2\cdot1 &= x\cdot2\cdot\frac{15}{2}&& \text{cancel out the denominators} \\[1 em]80+2x &= 15x&& \text{move the $ \color{blue}{ 15x } $ to the left side and $ \color{blue}{ 80 }$ to the right} \\[1 em]2x-15x &= -80&& \text{simplify left side} \\[1 em]-13x &= -80&& \text{ divide both sides by $ -13 $ } \\[1 em]x &= \frac{-80}{-13}&& \\[1 em]x &= \frac{80}{13}&& \\[1 em] \end{aligned} $$

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