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In which step was the subtraction property of equality applied?

[tex]\[
\begin{tabular}{|c|c|}
\hline Step & Statement \\
\hline 1 & \(\frac{z}{2}-7=-7\) \\
\hline 2 & \(\frac{z}{2}-7+7=-7+7\) \\
\hline 3 & \(\frac{z}{2}=0\) \\
\hline 4 & \(2 \cdot \frac{z}{2}=2 \cdot 0\) \\
\hline 5 & \(z=0\) \\
\hline
\end{tabular}
\][/tex]

A. Step 2
B. Step 3
C. Step 4
D. The subtraction property of equality was not applied to solve this equation.



Answer :

GinnyAnswer
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

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