To determine when the addition property of equality was applied, let's analyze each step of the solution provided:
1. Step 1: [tex]\(\frac{2}{3} x - 9 = -13\)[/tex]
This is the original equation.
2. Step 2: [tex]\(\frac{2}{3} x - 9 + 9 = -13 + 9\)[/tex]
This step involves adding 9 to both sides of the equation to isolate the term containing [tex]\(x\)[/tex]. This is a direct application of the addition property of equality, which states that you can add the same number to both sides of an equation without changing the equality.
3. Step 3: [tex]\(\frac{2}{3} x = -4\)[/tex]
The simplified result from Step 2.
4. Step 4: [tex]\(\frac{3}{2} \cdot \frac{2}{3} x = \frac{3}{2} \cdot (-4)\)[/tex]
Here, each side of the equation is multiplied by [tex]\(\frac{3}{2}\)[/tex] to solve for [tex]\(x\)[/tex].
5. Step 5: [tex]\(x = -6\)[/tex]
The final simplified value of [tex]\(x\)[/tex].
From the analysis, it is clear that the addition property of equality was applied in Step 2.
So, the correct answer is:
A. step 2
