$$ \begin{aligned} 35x+\frac{17}{2} &= 154&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot35x+2\cdot\frac{17}{2} &= 2\cdot154&& \text{cancel out the denominators} \\[1 em]70x+17 &= 308&& \text{ move 17 to the right } \\[1 em]70x &= 308-17&& \\[1 em]70x &= 291&& \text{ divide both sides by $ 70 $ } \\[1 em]x &= \frac{291}{70}&& \\[1 em] \end{aligned} $$

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