Select all of the equations below that are equivalent to: $\newline$ $-6 = mn$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $-2 = \frac{mn}{3}$ $\newline$ (B) $-5 = \frac{mn}{2}$ $\newline$ (C) $-3 = \frac{mn}{3}$ $\newline$ (D) $4 = \frac{mn}{-3}$

Full solution

Q. Select all of the equations below that are equivalent to:

\newline

-6 = mn

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

-2 = \frac{mn}{3}

\newline

(B)

-5 = \frac{mn}{2}

\newline

(C)

-3 = \frac{mn}{3}

\newline

(D)

4 = \frac{mn}{-3}

Analyze Equation: Step $1$ : Analyze the original equation and the transformation needed to check equivalency. $\newline$ Original equation: $-6 = mn$ . $\newline$ We need to determine if dividing or multiplying both sides of the equation by the same number results in the equations given in the choices.
Check Choice (A): Step $2$ : Check choice (A) $–2 = \frac{mn}{3}$ . $\newline$ Divide both sides of the original equation by $3$ : $\newline$ $\frac{-6}{3} = \frac{mn}{3}$ , $\newline$ $-2 = \frac{mn}{3}$ . $\newline$ This matches choice (A).
Check Choice (B): Step $3$ : Check choice (B) $–5 = \frac{mn}{2}$ . $\newline$ Divide both sides of the original equation by $2$ : $\newline$ $\frac{-6}{2} = \frac{mn}{2}$ , $\newline$ $-3 = \frac{mn}{2}$ . $\newline$ This does not match choice (B), so it's incorrect.
Check Choice (C): Step $4$ : Check choice $C$ $-3 = \frac{mn}{3}$ . $\newline$ Divide both sides of the original equation by $3$ : $\newline$ $\frac{-6}{3} = \frac{mn}{3}$ , $\newline$ $-2 = \frac{mn}{3}$ . $\newline$ This does not match choice $C$ , so it's incorrect.
Check Choice (D): Step $5$ : Check choice (D) $4 = \frac{mn}{-3}$ . Divide both sides of the original equation by $-3$ : $\frac{-6}{-3} = \frac{mn}{-3}$ , $2 = \frac{mn}{-3}$ . This does not match choice (D), so it's incorrect.