Let's analyze the given steps Paula used to solve the equation and determine between which two steps the division property of equality was applied.
- Step 1:
[tex]\[-4(x + 8) - 2x = 25\][/tex]
- Step 2:
[tex]\[-4x - 32 - 2x = 25\][/tex]
In this step, Paula distributed the [tex]\(-4\)[/tex] inside the parentheses.
- Step 3:
[tex]\[-6x - 32 = 25\][/tex]
Here, Paula combined like terms [tex]\(-4x\)[/tex] and [tex]\(-2x\)[/tex].
- Step 4:
[tex]\[-6x = 57\][/tex]
Paula added 32 to both sides to isolate the term with [tex]\(x\)[/tex].
- Step 5:
[tex]\[x = -9\frac{1}{2}\][/tex]
In this final step, Paula divided both sides by [tex]\(-6\)[/tex].
The division property of equality states that you can divide both sides of an equation by the same nonzero number. Paula uses this property between:
- Step 4: [tex]\[-6 x = 57\][/tex]
- Step 5: [tex]\(x = -9\frac{1}{2}\)[/tex]
Here, she divided both sides of the equation by [tex]\(-6\)[/tex] to solve for [tex]\(x\)[/tex].
Therefore, the correct answer is:
D. steps 4 and 5
