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Select the correct answer from each drop-down menu.

The given equation has been solved in the table:

[tex]\[
\begin{tabular}{|c|c|}
\hline
Step & Statement \\
\hline
1 & $-\frac{y}{2} - 6 = 15$ \\
\hline
2 & $-\frac{y}{2} - 6 + 6 = 15 + 6$ \\
\hline
3 & $-\frac{y}{2} = 21$ \\
\hline
4 & $-2 \cdot -\frac{y}{2} = -2 \cdot 21$ \\
\hline
5 & $y = -42$ \\
\hline
\end{tabular}
\][/tex]

Use the table to complete each statement:

1. In step 2, the [tex]$\square$[/tex] property of equality was applied.
2. In step 4, the [tex]$\square$[/tex] property of equality was applied.



Answer :

GinnyAnswer
Sure, let's analyze the steps provided in the table to identify the correct properties of equality applied at each step.

1. Original Equation:
[tex]\[ -\frac{y}{2} - 6 = 15 \][/tex]

2. Step 2:
[tex]\[ -\frac{y}{2} - 6 + 6 = 15 + 6 \][/tex]
Here, 6 is added to both sides of the equation. This is an application of the Addition property of equality.

3. Step 3:
[tex]\[ -\frac{y}{2} = 21 \][/tex]
The -6 and +6 on the left side cancel each other out, simplifying the equation to [tex]\(-\frac{y}{2} = 21\)[/tex].

4. Step 4:
[tex]\[ -2 \cdot -\frac{y}{2} = -2 \cdot 21 \][/tex]
Here, both sides of the equation are multiplied by -2. This is an application of the Multiplication property of equality.

5. Step 5:
[tex]\[ y = -42 \][/tex]
Simplifying the multiplication, we find that [tex]\(y = -42\)[/tex].

So, based on the steps above:

In step 2, the Addition property of equality was applied.

In step 4, the Multiplication property of equality was applied.

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