Problems 8-10: Solve each equation. Show your thinking. \( \begin{array}{ll}\text { 8. } \frac{1}{2}+x=2 & \text { 9. } \frac{2}{3} y=6\end{array} \) 10. \( 3=\frac{1}{4} b \)

Sure, let's solve each of the equations step by step. --- ### **Problem 8:** \[ \frac{1}{2} + x = 2 \] **Step 1:** Subtract \(\frac{1}{2}\) from both sides to isolate \(x\). \[ x = 2 - \frac{1}{2} \] **Step 2:** Convert \(2\) to a fraction with the same denominator to subtract easily. \[ 2 = \frac{4}{2} \] \[ x = \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \] **Final Answer:** \[ x = \frac{3}{2} \quad \text{or} \quad x = 1.5 \] --- ### **Problem 9:** \[ \frac{2}{3} y = 6 \] **Step 1:** To solve for \(y\), multiply both sides of the equation by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\). \[ y = 6 \times \frac{3}{2} \] **Step 2:** Multiply the numbers. \[ y = \frac{18}{2} = 9 \] **Final Answer:** \[ y = 9 \] --- ### **Problem 10:** \[ 3 = \frac{1}{4} b \] **Step 1:** To solve for \(b\), multiply both sides of the equation by \(4\), which is the reciprocal of \(\frac{1}{4}\). \[ 3 \times 4 = b \] **Step 2:** Perform the multiplication. \[ 12 = b \] **Final Answer:** \[ b = 12 \] --- If you have any more questions or need further clarification, feel free to ask!