Question

Identify the steps followed to solve the equation 5 - 3 (x + 3) = 11 - 8x
5 - 3x - 9 = 11 - 8x
-3x - 4 = 11 - 8x
5x - 4 = 11
5x = 15
x = 3
A) Distributive Property
B) Combine Like Terms
C) Multiplication Property of Equalities
D) Division Property of Equalities
E) Addition Property of Equalities
F) Subtraction Property of Equalities

Answer 1

To solve the equation step by step, let's identify the operations involved in each transformation:

1. **Original Equation**: \( 5 - 3(x + 3) = 11 - 8x \)
- This is where we start.

2. **Step 1**: \( 5 - 3(x + 3) = 11 - 8x \)
- We apply the **Distributive Property (A)** to expand the left side:
- \( 5 - 3x - 9 = 11 - 8x \)

3. **Step 2**: \( 5 - 3x - 9 = 11 - 8x \)
- Now, combine like terms on the left side:
- **Combine Like Terms (B)** results in:
- \( -3x - 4 = 11 - 8x \)

4. **Step 3**: \( -3x - 4 = 11 - 8x \)
- We can add \( 8x \) to both sides to isolate \( x \). This applies the **Addition Property of Equalities (E)**:
- \( -3x + 8x - 4 = 11 \) which simplifies to:
- \( 5x - 4 = 11 \)

5. **Step 4**: \( 5x - 4 = 11 \)
- Next, add \( 4 \) to both sides. This again uses the **Addition Property of Equalities (E)**:
- \( 5x - 4 + 4 = 11 + 4 \) simplifies to:
- \( 5x = 15 \)

6. **Step 5**: \( 5x = 15 \)
- Now, divide by \( 5 \) to solve for \( x \). This applies the **Division Property of Equalities (D)**:
- \( x = 3 \)

So, summarizing the steps:
- Step 1: A (Distributive Property)
- Step 2: B (Combine Like Terms)
- Step 3: E (Addition Property of Equalities twice: first to isolate \( x \), then to cancel \( -4 \))
- Step 4: D (Division Property of Equalities)

Thus, the correct operations used in each step in solving the equation are:
- **A)** Distributive Property
- **B)** Combine Like Terms
- **E)** Addition Property of Equalities
- **D)** Division Property of Equalities