To solve the problem of identifying when the subtraction property of equality was applied in the given steps, let's analyze the steps in detail.
1. Step 1: [tex]\(\frac{x}{2} - 7 = -7\)[/tex]
This is the initial equation provided.
2. Step 2: [tex]\(\frac{x}{2} - 7 + 7 = -7 + 7\)[/tex]
Here, 7 is added to both sides of the equation. Adding the same value to both sides of the equation is an essential aspect of maintaining equality, and in this context, it is effectively the same as subtracting [tex]\(-7\)[/tex]. This step simplifies the equation.
3. Step 3: [tex]\(\frac{x}{2} = 0\)[/tex]
After simplifying step 2, we get this equation, which no longer has the -7 term.
4. Step 4: [tex]\(2 \cdot \frac{x}{2} = 2 \cdot 0\)[/tex]
Here, both sides of the equation are multiplied by 2 to solve for [tex]\(x\)[/tex].
5. Step 5: [tex]\(x = 0\)[/tex]
This is the simplified result from step 4.
Therefore, the subtraction property of equality was applied in Step 2, where 7 was added to both sides, effectively eliminating the -7 on the left side and maintaining equality.
The correct answer is:
A. step 2
