Question

Question
When solving the equation 2(4x - 3) - 8 = 4 + 2x, which properties of equality would you need to apply in order? (1 point)
Responses

Multiplication, Division, Subtraction Properties
Multiplication, Division, Subtraction Properties

Subtraction, Multiplication, Addition Properties
Subtraction, Multiplication, Addition Properties

Distribute, Subtraction, Addition, Division Properties
Distribute, Subtraction, Addition, Division Properties

Addition, Multiplication, Subtraction Properties

Answer 1

To solve the equation \(2(4x - 3) - 8 = 4 + 2x\), we apply the following steps, which correspond to properties of equality:

1. **Distribute**: Apply the distributive property to the left side:
\[
2(4x - 3) \to 8x - 6
\]
So, the equation becomes:
\[
8x - 6 - 8 = 4 + 2x
\]

2. **Combine like terms**: Simplify the left side:
\[
8x - 14 = 4 + 2x
\]

3. **Subtraction**: Use the subtraction property to isolate \(x\):
\[
8x - 2x - 14 = 4 \implies 6x - 14 = 4
\]

4. **Addition**: Use the addition property to simplify further:
\[
6x - 14 + 14 = 4 + 14 \implies 6x = 18
\]

5. **Division**: Finally, apply the division property to solve for \(x\):
\[
x = 3
\]

Based on these steps, the correct response would be:

**Distribute, Subtraction, Addition, Division Properties**.