$$x+\frac{x}{2}+1 = 19$$

$$ \begin{aligned} x+\frac{x}{2}+1 &= 19&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x+2 \cdot \frac{x}{2}+2\cdot1 &= 2\cdot19&& \text{cancel out the denominators} \\[1 em]2x+x+2 &= 38&& \text{simplify left side} \\[1 em]3x+2 &= 38&& \text{ move 2 to the right } \\[1 em]3x &= 38-2&& \\[1 em]3x &= 36&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{36}{3}&& \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

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