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 an equation by the coefficient of the variable.

Step2: Analyze each step transition

• Steps 1 to 2: This is the distributive property (distributing -4 to \( x \) and 8 in \( -4(x + 8) \)).
• Steps 2 to 3: This is combining like terms (\( -4x-2x=-6x \)).
• Steps 3 to 4: This is the addition property of equality (adding 32 to both sides: \( -6x-32 + 32=25 + 32\Rightarrow-6x = 57 \)).
• Steps 4 to 5: Here, we have \( -6x=57 \). To solve for \( x \), we divide both sides by -6 (using the division property of equality): \( \frac{-6x}{-6}=\frac{57}{-6}\Rightarrow x=-9\frac{1}{2} \).

Answer:

D. steps 4 and 5