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.
