Question

select the correct answer.
paula used these steps to solve an equation:
step 1: $-4(x + 8) - 2x = 25$
step 2: $-4x - 32 - 2x = 25$
step 3: $-6x - 32 = 25$
step 4: $-6x = 57$
step 5: $x = -9\frac{1}{2}$
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

Explanation:

Step1: Recall the division property of equality

The division property of equality states that if \(a = b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\). This is used to isolate the variable by dividing both sides of the equation by the coefficient of the variable.

Step2: Analyze each step pair

• Steps 1 and 2: Step 1 is \(-4(x + 8)-2x = 25\), Step 2 is \(-4x-32 - 2x=25\). This is the distributive property (distributing \(-4\) over \(x + 8\)), not division property.
• Steps 2 and 3: Step 2 is \(-4x-32 - 2x=25\), Step 3 is \(-6x-32 = 25\). This is combining like terms (\(-4x-2x=-6x\)), not division property.
• Steps 3 and 4: Step 3 is \(-6x-32 = 25\), Step 4 is \(-6x=57\). This is the addition property of equality (adding 32 to both sides), not division property.
• Steps 4 and 5: Step 4 is \(-6x = 57\), Step 5 is \(x=-\frac{57}{6}=-\frac{19}{2}=-9\frac{1}{2}\). Here, we divide both sides of the equation \(-6x = 57\) by \(-6\) (using the division property of equality) to solve for \(x\).

Answer:

D. steps 4 and 5