$$ \begin{aligned} \frac{138}{60} &= \frac{x}{6}+\frac{10-x}{4}&& \text{multiply ALL terms by } \color{blue}{ 60 }. \\[1 em]60\cdot\frac{138}{60} &= 60 \cdot \frac{x}{6}+60\frac{10-x}{4}&& \text{cancel out the denominators} \\[1 em]138 &= 10x-15x+150&& \text{simplify right side} \\[1 em]138 &= -5x+150&& \text{ swap the left and right side of the equation } \\[1 em]-5x+150 &= 138&& \text{ move 150 to the right } \\[1 em]-5x &= 138-150&& \\[1 em]-5x &= -12&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{-12}{-5}&& \\[1 em]x &= \frac{12}{5}&& \\[1 em] \end{aligned} $$

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