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** \[ -4(r + 2) = 4(2 - 2r) \] **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: Combine like terms.** First, let's get all terms containing \( r \) on one side and constants on the other. We'll add \( 8r \) to both sides and add \( 8 \) to both sides to isolate \( r \). \[ -4r + 8r - 8 + 8 = 8 - 8r + 8r \] \[ 4r = 16 \] **Step 3: Solve for \( r \).** Divide both sides by 4: \[ r = \frac{16}{4} = 4 \] **Answer:** \( r = 4 \) --- ### **Problem 10** \[ 1.3 + 6d = 2.7 - 8d \] **Step 1: Get all terms containing \( d \) on one side and constants on the other.** Add \( 8d \) to both sides and subtract \( 1.3 \) from both sides: \[ 1.3 + 6d + 8d = 2.7 - 8d + 8d \] \[ 1.3 + 14d = 2.7 \] \[ 14d = 2.7 - 1.3 \] \[ 14d = 1.4 \] **Step 2: Solve for \( d \).** Divide both sides by 14: \[ d = \frac{1.4}{14} = 0.1 \] **Answer:** \( d = 0.1 \) --- If you have any further questions or need additional explanations, feel free to ask!