Problems 9-10: Solve each equation. Show your thinking. \( \begin{array}{ll}9 .-4(r+2)=4(2-2 r) & \text { 10. } 1.3+6 d=2.7-8 d\end{array} \)

Sure, let's solve each equation step-by-step. --- ### **Problem 9** **Equation:** \[ -4(r + 2) = 4(2 - 2r) \] **Step 1: Distribute the multiplication on both sides.** \[ -4 \cdot r - 4 \cdot 2 = 4 \cdot 2 - 4 \cdot 2r \] \[ -4r - 8 = 8 - 8r \] **Step 2: Get all terms containing \( r \) on one side and constants on the other.** Add \( 8r \) to both sides to move the \( r \)-terms to the left: \[ -4r + 8r - 8 = 8 \] \[ 4r - 8 = 8 \] **Step 3: Isolate \( r \).** Add \( 8 \) to both sides to move the constant term: \[ 4r = 16 \] Divide both sides by \( 4 \): \[ r = 4 \] --- ### **Problem 10** **Equation:** \[ 1.3 + 6d = 2.7 - 8d \] **Step 1: Get all terms containing \( d \) on one side and constants on the other.** Add \( 8d \) to both sides to move the \( d \)-terms to the left: \[ 1.3 + 6d + 8d = 2.7 \] \[ 1.3 + 14d = 2.7 \] **Step 2: Isolate the \( d \)-term.** Subtract \( 1.3 \) from both sides: \[ 14d = 2.7 - 1.3 \] \[ 14d = 1.4 \] **Step 3: Solve for \( d \).** Divide both sides by \( 14 \): \[ d = \frac{1.4}{14} = 0.1 \] --- **Final Answers:** - **Problem 9:** \( r = 4 \) - **Problem 10:** \( d = 0.1 \)