$$2x+\frac{7}{12}+x+\frac{5}{12} = x+\frac{6}{8}$$

$$ \begin{aligned} 2x+\frac{7}{12}+x+\frac{5}{12} &= x+\frac{6}{8}&& \text{multiply ALL terms by } \color{blue}{ 24 }. \\[1 em]24\cdot2x+24\cdot\frac{7}{12}+24x+24\cdot\frac{5}{12} &= 24x+24\cdot\frac{6}{8}&& \text{cancel out the denominators} \\[1 em]48x+14+24x+10 &= 24x+18&& \text{simplify left side} \\[1 em]72x+24 &= 24x+18&& \text{move the $ \color{blue}{ 24x } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]72x-24x &= 18-24&& \text{simplify left and right hand side} \\[1 em]48x &= -6&& \text{ divide both sides by $ 48 $ } \\[1 em]x &= -\frac{6}{48}&& \\[1 em]x &= -\frac{1}{8}&& \\[1 em] \end{aligned} $$

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