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

Question

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

UpStudy AI · Accepted Answer

Sure, let's solve each equation step-by-step.

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### **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 $$ 4 $$:

$$
r = 4
$$

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### **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 $$ 14 $$:

$$
d = \frac{1.4}{14} = 0.1
$$

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**Final Answers:**
- **Problem 9:** $$ r = 4 $$
- **Problem 10:** $$ d = 0.1 $$
**Problem 9:** $$ r = 4 $$ **Problem 10:** $$ d = 0.1 $$

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