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------------------------------------------------ Which of the following indicates the division property of equality when solving [tex]-12x = 48[/tex]?

A) [tex]x = \frac{1}{4}[/tex]

B) [tex]\frac{-12x}{-12} = \frac{48}{-12}[/tex]

C) [tex]-12x = \frac{48}{-12}[/tex]

D) [tex]x = \frac{48}{12}[/tex]

To solve the equation [tex]$-12x = 48$[/tex] using the division property of equality, follow these steps:

1. Understand the Division Property of Equality: This property states that you can divide both sides of an equation by the same nonzero number, and the equality will still hold true.

2. Apply the Division Property: To isolate the variable [tex]$x$[/tex], you need to divide both sides of the equation by [tex]$-12$[/tex] because [tex]$-12$[/tex] is the coefficient of [tex]$x$[/tex].

[tex]\[
\frac{-12x}{-12} = \frac{48}{-12}
\][/tex]

3. Simplify Both Sides:
- On the left side, [tex]$\frac{-12x}{-12}$[/tex] simplifies to [tex]$x$[/tex].
- On the right side, [tex]$\frac{48}{-12}$[/tex] simplifies to [tex]$-4$[/tex].

So, you get:

[tex]\[
x = -4
\][/tex]

4. Identify the Correct Choice: Among the given options, the expression [tex]$\frac{-12x}{-12} = \frac{48}{-12}$[/tex] represents the correct use of the division property of equality. Hence, the correct answer is option B.

Therefore, the solution indicates that option B) [tex]$\frac{-12x}{-12} = \frac{48}{-12}$[/tex] is the choice that applies the division property of equality correctly.