Question

Identify the steps followed to solve the equation 5-3 (x+3) =11-8x
(5 points)

5-3x-9=11-8x ____

-3x-4 =11-8x ____

5x-4=11 ____

5x = 15 ____

x=3 ____

:: Distributive Property

:: Multiplication Property of Equalities

:: Addition Property of Equalities

:: Combine Like Terms

:: Division Property of Equalities

:: Subtraction Property of Equalities

Answer 1

Let's break down the steps taken to solve the equation \(5 - 3(x + 3) = 11 - 8x\) and match them with the appropriate properties you listed.

1. **Start with the original equation:**
\[
5 - 3(x + 3) = 11 - 8x
\]
- **Property:** None applied yet.

2. **Apply the Distributive Property:**
\[
5 - 3x - 9 = 11 - 8x
\]
- **Matched Property:** Distributive Property

3. **Combine Like Terms:**
\[
-3x - 4 = 11 - 8x
\]
- **Matched Property:** Combine Like Terms

4. **Add \(8x\) to both sides (using the Addition Property):**
\[
5x - 4 = 11
\]
- **Matched Property:** Addition Property of Equalities

5. **Add \(4\) to both sides (using the Addition Property):**
\[
5x = 15
\]
- **Matched Property:** Addition Property of Equalities

6. **Divide both sides by \(5\):**
\[
x = 3
\]
- **Matched Property:** Division Property of Equalities

Here’s the summarized allocation of each step with properties:

1. \(5 - 3(x + 3) = 11 - 8x\) - No property applied.
2. \(5 - 3x - 9 = 11 - 8x\) - **Distributive Property**
3. \(-3x - 4 = 11 - 8x\) - **Combine Like Terms**
4. \(5x - 4 = 11\) - **Addition Property of Equalities**
5. \(5x = 15\) - **Addition Property of Equalities**
6. \(x = 3\) - **Division Property of Equalities**

No additional properties were needed for steps 1, and at step 4, both the addition to isolate terms and combining like terms were utilized.