$$ \begin{aligned} 5x+\frac{1}{2}(24x+72) &= 206&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot5x+2 \cdot \frac{1}{2}(24x+72) &= 2\cdot206&& \text{cancel out the denominators} \\[1 em]10x+24x+72 &= 412&& \text{simplify left side} \\[1 em]34x+72 &= 412&& \text{ move 72 to the right } \\[1 em]34x &= 412-72&& \\[1 em]34x &= 340&& \text{ divide both sides by $ 34 $ } \\[1 em]x &= \frac{340}{34}&& \\[1 em]x &= 10&& \\[1 em] \end{aligned} $$

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