$$ \begin{aligned} 1 &= \frac{2}{5}(9x+10)&& \text{simplify right side} \\[1 em]1 &= \frac{18x+20}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot1 &= 5 \cdot \frac{18x+20}{5}&& \text{cancel out the denominators} \\[1 em]5 &= 18x+20&& \text{ swap the left and right side of the equation } \\[1 em]18x+20 &= 5&& \text{ move 20 to the right } \\[1 em]18x &= 5-20&& \\[1 em]18x &= -15&& \text{ divide both sides by $ 18 $ } \\[1 em]x &= -\frac{15}{18}&& \\[1 em]x &= -\frac{5}{6}&& \\[1 em] \end{aligned} $$

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