$$ \begin{aligned} 2x+2\cdot\frac{7}{16} &= 1&& \text{multiply ALL terms by } \color{blue}{ 16 }. \\[1 em]16\cdot2x+16\cdot2\cdot\frac{7}{16} &= 16\cdot1&& \text{cancel out the denominators} \\[1 em]32x+14 &= 16&& \text{ move 14 to the right } \\[1 em]32x &= 16-14&& \\[1 em]32x &= 2&& \text{ divide both sides by $ 32 $ } \\[1 em]x &= \frac{2}{32}&& \\[1 em]x &= \frac{1}{16}&& \\[1 em] \end{aligned} $$

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