Let's analyze the given steps to determine which properties of equality were applied.
Here is the equation and steps again for reference:
[tex]\[
\begin{tabular}{|c|c|}
\hline Step & Statement \\
\hline 1 & \(\frac{z}{4}+5=23\) \\
\hline 2 & \(\frac{z}{4}+5-5=23-5\) \\
\hline 3 & \(\frac{z}{4}=18\) \\
\hline 4 & \(4 \cdot \frac{z}{4}=4 \cdot 18\) \\
\hline 5 & \(z=72\) \\
\hline
\end{tabular}
\][/tex]
### Explanation of Steps:
Step 2:
The operation involves subtracting 5 from both sides of the equation:
[tex]\[
\frac{z}{4} + 5 - 5 = 23 - 5
\][/tex]
Simplifies to:
[tex]\[
\frac{z}{4} = 18
\][/tex]
Here, the subtraction property of equality was applied. This property states that if you subtract the same number from both sides of an equation, the equality is still maintained.
Step 4:
The operation involves multiplying both sides by 4:
[tex]\[
4 \cdot \frac{z}{4} = 4 \cdot 18
\][/tex]
Simplifies to:
[tex]\[
z = 72
\][/tex]
Here, the multiplication property of equality was applied. This property states that if you multiply both sides of an equation by the same number, the equality is still maintained.
### Conclusion:
1. In step 2, the subtraction property of equality was applied.
2. In step 4, the multiplication property of equality was applied.
So, the complete statements are:
- In step 2, the subtraction property of equality was applied.
- In step 4, the multiplication property of equality was applied.
