$$ \begin{aligned} 44+x &= \frac{3x-5}{6}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot44+6x &= 6 \cdot \frac{3x-5}{6}&& \text{cancel out the denominators} \\[1 em]264+6x &= 3x-5&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 264 }$ to the right} \\[1 em]6x-3x &= -5-264&& \text{simplify left and right hand side} \\[1 em]3x &= -269&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{269}{3}&& \\[1 em] \end{aligned} $$

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