To determine which property is used in the first step of solving the equation [tex]\(3(x - 7) = 2 - x\)[/tex], let's examine the initial equation and understand the properties involved.
Given the equation:
[tex]\[3(x - 7) = 2 - x\][/tex]
### Step-by-Step Solution:
1. Initial Equation:
We start with:
[tex]\[3(x - 7) = 2 - x\][/tex]
2. Applying the First Property:
- Observe the left side of the equation: [tex]\(3(x - 7)\)[/tex]
- Here, we need to expand the expression [tex]\(3(x - 7)\)[/tex] to simplify it.
3. Distributive Property:
- The distributive property states that:
[tex]\[a(b + c) = ab + ac\][/tex]
- For the given equation [tex]\(3(x - 7)\)[/tex], applying the distributive property, we get:
[tex]\[3(x - 7) = 3 \cdot x + 3 \cdot (-7)\][/tex]
[tex]\[3x - 21\][/tex]
4. Result:
- After distributing, the equation becomes:
[tex]\[3x - 21 = 2 - x\][/tex]
So, the property used in the first step is the Distributive Property.
Therefore, the correct option is:
B) Distributive Property.
