$$ \begin{aligned} \frac{2}{2x+2} &= 10&& \text{multiply ALL terms by } \color{blue}{ 2x+2 }. \\[1 em](2x+2)\cdot\frac{2}{2x+2} &= (2x+2)\cdot10&& \text{cancel out the denominators} \\[1 em]2 &= 20x+20&& \text{ swap the left and right side of the equation } \\[1 em]20x+20 &= 2&& \text{ move 20 to the right } \\[1 em]20x &= 2-20&& \\[1 em]20x &= -18&& \text{ divide both sides by $ 20 $ } \\[1 em]x &= -\frac{18}{20}&& \\[1 em]x &= -\frac{9}{10}&& \\[1 em] \end{aligned} $$

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