$$ \begin{aligned} 2x-\frac{15}{7} &= 48-\frac{1}{7}x&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7\cdot2x-7\cdot\frac{15}{7} &= 7\cdot48-7 \cdot \frac{1}{7}x&& \text{cancel out the denominators} \\[1 em]14x-15 &= 336-x&& \text{move the $ \color{blue}{ -x } $ to the left side and $ \color{blue}{ -15 }$ to the right} \\[1 em]14x+x &= 336+15&& \text{simplify left and right hand side} \\[1 em]15x &= 351&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{351}{15}&& \\[1 em]x &= \frac{117}{5}&& \\[1 em] \end{aligned} $$

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