Question
9. \( -4(r+2)=4(2-2 r) \quad \) 10. \( 1.3+6 d=2.7-8 d \)
Ask by Chambers Lowe. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**Problem 9:**
\( r = 4 \)
**Problem 10:**
\( d = 0.1 \)
Solution
Sure, let's solve each equation step by step.
---
### **Problem 9:**
\[
-4(r + 2) = 4(2 - 2r)
\]
**Step 1: Distribute the constants on both sides.**
\[
-4 \cdot r - 4 \cdot 2 = 4 \cdot 2 - 4 \cdot 2r
\]
\[
-4r - 8 = 8 - 8r
\]
**Step 2: Get all \( r \)-terms on one side and constants on the other.**
\[
-4r + 8r = 8 + 8
\]
\[
4r = 16
\]
**Step 3: Solve for \( r \).**
\[
r = \frac{16}{4} = 4
\]
**Answer:** \( r = 4 \)
---
### **Problem 10:**
\[
1.3 + 6d = 2.7 - 8d
\]
**Step 1: Get all \( d \)-terms on one side and constants on the other.**
Add \( 8d \) to both sides:
\[
1.3 + 6d + 8d = 2.7
\]
\[
1.3 + 14d = 2.7
\]
**Step 2: Subtract \( 1.3 \) from both sides to isolate the \( d \)-terms.**
\[
14d = 2.7 - 1.3
\]
\[
14d = 1.4
\]
**Step 3: Solve for \( d \).**
\[
d = \frac{1.4}{14} = 0.1
\]
**Answer:** \( d = 0.1 \)
---
If you have any further questions or need additional explanations, feel free to ask!
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Did you know that solving linear equations like \( -4(r+2)=4(2-2r) \) can be traced back to the ancient Babylonians, who were among the first to use algebraic methods? They employed geometric solutions to quadratic equations, which laid the groundwork for modern algebra as we know it! In real life, mastering linear equations is essential for budgeting and finance, like tracking expenses or calculating profits. When you set an equation to find out how many items you need to sell to break even or how much money to save monthly to reach a goal, you're using these principles! So, next time you balance your bank account or plan a trip, remember you're tapping into a vital math skill!
