Certainly! Let's analyze the steps provided in the table to determine which property of equality was applied in each step.
1. Starting equation: [tex]\( -\frac{y}{2} - 6 = 15 \)[/tex]
2. Step 2: [tex]\( -\frac{y}{2} - 6 + 6 = 15 + 6 \)[/tex]
- Here, we are adding 6 to both sides of the equation. This operation is done to isolate the term containing [tex]\( y \)[/tex] on one side. The property of equality applied in this step is Addition.
3. Step 3: [tex]\( -\frac{y}{2} = 21 \)[/tex]
- This is a simplified form after performing the addition in the previous step.
4. Step 4: [tex]\( -2 \cdot -\frac{y}{2} = -2 \cdot 21 \)[/tex]
- Here, we are multiplying both sides of the equation by [tex]\(-2\)[/tex]. This operation is done to get rid of the fraction and solve for [tex]\( y \)[/tex]. The property of equality applied in this step is Multiplication.
5. Step 5: [tex]\( y = -42 \)[/tex]
- This is the result after performing the multiplication in the previous step.
Based on these steps, the complete statements are:
In step 2, the Addition property of equality was applied.
In step 4, the Multiplication property of equality was applied.
