Find accurate and reliable answers to your questions on IDNLearn.com. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.

Select the correct answer.

Paula used these steps to solve an equation:

Step 1: [tex]\(-4(x+8) - 2x = 25\)[/tex]

Step 2: [tex]\(-4x - 32 - 2x = 25\)[/tex]

Step 3: [tex]\(-6x - 32 = 25\)[/tex]

Step 4: [tex]\(-6x = 57\)[/tex]

Step 5: [tex]\(x = -9 \frac{1}{2}\)[/tex]

Between which two steps did Paula use the division property of equality?

A. steps 1 and 2

B. steps 2 and 3

C. steps 3 and 4

D. steps 4 and 5


Sagot :

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