$$ \begin{aligned} 9+\frac{7}{2}g &= 11-\frac{1}{2}g&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot9+2 \cdot \frac{7}{2}g &= 2\cdot11-2 \cdot \frac{1}{2}g&& \text{cancel out the denominators} \\[1 em]18+7g &= 22-g&& \text{move the $ \color{blue}{ -g } $ to the left side and $ \color{blue}{ 18 }$ to the right} \\[1 em]7g+g &= 22-18&& \text{simplify left and right hand side} \\[1 em]8g &= 4&& \text{ divide both sides by $ 8 $ } \\[1 em]g &= \frac{4}{8}&& \\[1 em]g &= \frac{1}{2}&& \\[1 em] \end{aligned} $$

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