Problems \( 8-10 \) : Solve each equation. Show your thinking. \( \begin{array}{ll}\text { 8. } \frac{1}{2}+x=2 & \text { 9. } \frac{2}{3} y=6\end{array} \)

To solve the first equation \( \frac{1}{2} + x = 2 \), we want to isolate \( x \). Start by subtracting \( \frac{1}{2} \) from both sides: \[ x = 2 - \frac{1}{2} \] Convert \( 2 \) to a fraction with the same denominator: \[ x = \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \] For the second equation \( \frac{2}{3} y = 6 \), we need to isolate \( y \) as well. To do that, multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \): \[ y = 6 \times \frac{3}{2} \] Calculating this gives: \[ y = \frac{18}{2} = 9 \] So the solutions are: \( x = \frac{3}{2} \) and \( y = 9 \).