Ashleenbondidn
Answered

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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 :

GinnyAnsweridn
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
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