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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 :

GinnyAnswer
Let's carefully analyze each step of the solution to determine where the division property of equality was applied:

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

Step 2:
Distribute [tex]\(-4\)[/tex] through [tex]\((x+8)\)[/tex], which gives: [tex]\(-4x - 32 - 2x = 25\)[/tex]

Step 3:
Combine like terms [tex]\(-4x\)[/tex] and [tex]\(-2x\)[/tex], resulting in: [tex]\(-6x - 32 = 25\)[/tex]

Step 4:
To isolate [tex]\(x\)[/tex], add 32 to both sides of the equation: [tex]\(-6x = 57\)[/tex]

Step 5:
Divide both sides by [tex]\(-6\)[/tex] to solve for [tex]\(x\)[/tex], which results in: [tex]\(x = -9\frac{1}{2}\)[/tex] or [tex]\(x = -9.5\)[/tex]

The division property of equality is used when both sides of the equation are divided by the same nonzero number.

In this solution, we see that the division property was applied between Step 4 and Step 5, where both sides of the equation [tex]\(-6x = 57\)[/tex] were divided by [tex]\(-6\)[/tex] to solve for [tex]\(x\)[/tex].

Therefore, the correct answer is:

D. steps 4 and 5
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