To determine between which steps Paula used the division property of equality, let’s review the steps in detail:
Step 1: [tex]\(-4(x + 8) - 2x = 25\)[/tex]
Paula begins with the original equation.
Step 2: [tex]\(-4x - 32 - 2x = 25\)[/tex]
Here, Paula has distributed the [tex]\(-4\)[/tex] across [tex]\(x + 8\)[/tex], resulting in [tex]\(-4x - 32\)[/tex]. Nothing has been divided yet; this step is simply the application of the distributive property.
Step 3: [tex]\(-6x - 32 = 25\)[/tex]
Paula combines like terms [tex]\(-4x\)[/tex] and [tex]\(-2x\)[/tex] to get [tex]\(-6x\)[/tex]. Again, no division has occurred as this step involves combining terms.
Step 4: [tex]\(-6x = 57\)[/tex]
Paula has added [tex]\(32\)[/tex] to both sides of the equation to isolate the term with [tex]\(x\)[/tex]. This is the addition property of equality.
Step 5: [tex]\(x = -9 \frac{1}{2}\)[/tex]
In the final step, Paula divides both sides of the equation by [tex]\(-6\)[/tex] to solve for [tex]\(x\)[/tex]. This is where the division property of equality is used.
Thus, the division property of equality is used between step 4 and step 5.
So the correct answer is:
D. steps 4 and 5
