Select all of the equations below that are equivalent to: $\newline$ $-71p = 25$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $-\frac{71p}{5} = 5$ $\newline$ (B) $-\frac{71p}{-5} = -4$ $\newline$ (C) $-\frac{71p}{-5} = -5$ $\newline$ (D) $-\frac{71p}{5} = 3$

Full solution

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

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-71p = 25

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Use properties of equality.

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\newline

Multi-select Choices:

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(A)

-\frac{71p}{5} = 5

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(B)

-\frac{71p}{-5} = -4

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(C)

-\frac{71p}{-5} = -5

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(D)

-\frac{71p}{5} = 3

Analyze Equation and Choices: Step $1$ : Analyze the original equation and the choices given. $\newline$ Original equation: $-71p = 25$ . $\newline$ Choices involve dividing both sides of the original equation by a number.
Check Choice (A): Step $2$ : Check choice (A) $\frac{-71p}{5} = 5$ . $\newline$ Divide both sides of the original equation by $5$ : $\newline$ $\frac{(–71p)}{5} = \frac{25}{5}$ , $\newline$ $–14.2p = 5$ . $\newline$ This does not match choice (A) since $–14.2p \neq 5$ .
Check Choice (B): Step $3$ : Check choice (B) $\frac{-71p}{-5} = -4$ . $\newline$ Divide both sides of the original equation by $-5$ : $\newline$ $\frac{(-71p)}{-5} = \frac{25}{-5}$ , $\newline$ $14.2p = -5$ . $\newline$ This does not match choice (B) since $14.2p \neq -4$ .
Check Choice (C): Step $4$ : Check choice (C) $\frac{-71p}{-5} = -5$ . Continue from the calculation in Step $3$ : $14.2p = -5$ . This matches choice (C) since $14.2p = -5$ .
Check Choice (D): Step $5$ : Check choice (D) $\frac{-71p}{5} = 3$ . $\newline$ Divide both sides of the original equation by $5$ : $\newline$ $\frac{(\text{–}71p)}{5} = \frac{25}{5}$ , $\newline$ $\text{–}14.2p = 5$ . $\newline$ This does not match choice (D) since $\text{–}14.2p \neq 3$ .