$$ \begin{aligned} \frac{1}{5x+2} &= 8&& \text{multiply ALL terms by } \color{blue}{ 5x+2 }. \\[1 em](5x+2)\cdot\frac{1}{5x+2} &= (5x+2)\cdot8&& \text{cancel out the denominators} \\[1 em]1 &= 40x+16&& \text{ swap the left and right side of the equation } \\[1 em]40x+16 &= 1&& \text{ move 16 to the right } \\[1 em]40x &= 1-16&& \\[1 em]40x &= -15&& \text{ divide both sides by $ 40 $ } \\[1 em]x &= -\frac{15}{40}&& \\[1 em]x &= -\frac{3}{8}&& \\[1 em] \end{aligned} $$

This page was created using