Problems 9-10: Solve each equation. Show your thinking.

Ask by Harper Savage. in the United States

Jan 23,2025

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**

$$
-4(r + 2) = 4(2 - 2r)
$$

**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:** $$ d = 0.1 $$

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If you have any further questions or need additional explanations, feel free to ask!
**Problem 9:** $$ r = 4 $$ **Problem 10:** $$ d = 0.1 $$

Problems 9-10: Solve each equation. Show your thinking.

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