Select all of the equations below that are equivalent to: $\newline$ $j - k = -3$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $(j - k) \cdot 28 = -84$ $\newline$ (B) $(j - k) \cdot -32 = 96$ $\newline$ (C) $(j - k) \cdot -31 = 93$ $\newline$ (D) $9(j - k) = -27$

Full solution

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

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j - k = -3

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Use properties of equality.

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Multi-select Choices:

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(A)

(j - k) \cdot 28 = -84

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(B)

(j - k) \cdot -32 = 96

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(C)

(j - k) \cdot -31 = 93

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(D)

9(j - k) = -27

Analyze Equation: Step $1$ : Analyze the given equation and the properties of equality. $\newline$ The original equation is $j - k = -3$ . We need to check if multiplying both sides of this equation by a constant gives the equations in the choices.
Check Choice (A): Step $2$ : Check choice (A). Multiply both sides of $j − k = −3$ by $28$ : $(j − k) \cdot 28 = −3 \cdot 28$ Calculate $−3 \cdot 28 = −84$ . Check if $(j − k) \cdot 28 = −84$ matches choice (A).
Check Choice (B): Step $3$ : Check choice (B). $\newline$ Multiply both sides of $j - k = -3$ by $-32$ : $\newline$ $(j - k) \cdot -32 = -3 \cdot -32$ $\newline$ Calculate $-3 \cdot -32 = 96$ . $\newline$ Check if $(j - k) \cdot -32 = 96$ matches choice (B).
Check Choice (C): Step $4$ : Check choice (C). $\newline$ Multiply both sides of $j - k = -3$ by $-31$ : $\newline$ $(j - k) \cdot -31 = -3 \cdot -31$ $\newline$ Calculate $-3 \cdot -31 = 93$ . $\newline$ Check if $(j - k) \cdot -31 = 93$ matches choice (C).
Check Choice (D): Step $5$ : Check choice (D). Multiply both sides of $j - k = -3$ by $9$ : $9(j - k) = -3 \cdot 9$ Calculate $-3 \cdot 9 = -27$ . Check if $9(j - k) = -27$ matches choice (D).