Select all of the equations below that are equivalent to: $\newline$ $-10 = gh$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $4 = \frac{gh}{-5}$ $\newline$ (B) $-2 = \frac{gh}{5}$ $\newline$ (C) $5 = \frac{gh}{-2}$ $\newline$ (D) $2 = \frac{gh}{-5}$

Full solution

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

\newline

-10 = gh

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

4 = \frac{gh}{-5}

\newline

(B)

-2 = \frac{gh}{5}

\newline

(C)

5 = \frac{gh}{-2}

\newline

(D)

2 = \frac{gh}{-5}

Analyze Equation and Choices: Step $1$ : Analyze the given equation and the choices. $\newline$ We start with the equation $-10 = gh$ . We need to find which of the choices are equivalent by using properties of equality, specifically division in this case.
Check Choice (A): Step $2$ : Check choice (A) $4 = \frac{gh}{-5}$ . Divide both sides of the original equation by $-5$ : $\frac{-10}{-5} = \frac{gh}{-5}$ . Simplify the left side: $2 = \frac{gh}{-5}$ . This does not match choice (A), which states $4 = \frac{gh}{-5}$ .
Check Choice (B): Step $3$ : Check choice (B) $-2 = \frac{gh}{5}$ . $\newline$ Divide both sides of the original equation by $5$ : $-10 / 5 = \frac{gh}{5}$ . Simplify the left side: $-2 = \frac{gh}{5}$ . This matches choice (B).
Check Choice (C): Step $4$ : Check choice (C) $5 = \frac{gh}{-2}$ . $\newline$ Divide both sides of the original equation by $-2$ : $\frac{-10}{-2} = \frac{gh}{-2}$ . Simplify the left side: $5 = \frac{gh}{-2}$ . This matches choice (C).
Check Choice (D): Step $5$ : Check choice (D) $2 = \frac{gh}{-5}$ . $\newline$ We already calculated this in Step $2$ . The result was $2 = \frac{gh}{-5}$ , which matches choice (D).