To determine which step involves the application of the subtraction property of equality, let's analyze each step one by one.
1. Step 1: [tex]\(\frac{\pi}{2}-7=-7\)[/tex]
This is the initial equation provided.
2. Step 2: [tex]\(\frac{z}{2}-7+7=-7+7\)[/tex]
Here, both sides of the equation from step 1 have added 7. This step applies the subtraction property of equality by adding the same number (7) to both sides in order to eliminate the -7 on the left side.
3. Step 3: [tex]\(\frac{z}{2}=0\)[/tex]
This step simplifies the equation from step 2 by combining like terms. After [tex]\(~\frac{z}{2}-7 + 7 =~\frac{z}{2}\)[/tex] and [tex]\(~-7+7~=~0\)[/tex], it simplifies to [tex]\(~\frac{z}{2}~=~0\)[/tex].
4. Step 4: [tex]\(2 \cdot \frac{z}{2}=2 \cdot 0\)[/tex]
Here, both sides of the equation from step 3 are multiplied by 2 to solve for [tex]\(z\)[/tex].
5. Step 5: [tex]\(z=0\)[/tex]
This step provides the final solution of the equation.
By analyzing the steps, it is evident that step 2 is where the subtraction property of equality (adding 7 to both sides) is applied. Thus, the correct answer is:
A. step 2
