Select all of the equations below that are equivalent to: $\newline$ $-19 = -25k$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $76 = -4 \cdot -25k$ $\newline$ (B) $-54 = -25k \cdot 3$ $\newline$ (C) $-38 = 2 \cdot -25k$ $\newline$ (D) $-2 \cdot -19 = 50k$

Full solution

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

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-19 = -25k

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Use properties of equality.

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Multi-select Choices:

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(A)

76 = -4 \cdot -25k

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(B)

-54 = -25k \cdot 3

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(C)

-38 = 2 \cdot -25k

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(D)

-2 \cdot -19 = 50k

Check Multiplication by $-4$ : To determine if an equation is equivalent to $-19 = -25k$ , we can perform operations that maintain equality. For choice (A), we check if multiplying both sides of the original equation by $-4$ gives us $76 = -4 \cdot -25k$ . $\newline$ Calculation: $-19 \times (-4) = -25k \times (-4)$ $\newline$ $76 = 100k$ $\newline$ This is not equivalent to the original equation.
Check Multiplication by $3$ : For choice (B), we check if multiplying the original equation by $3$ gives us $-54 = -25k \cdot 3$ . $\newline$ Calculation: $-19 \times 3 = -25k \times 3$ $\newline$ $-57 = -75k$ $\newline$ This is not equivalent to the original equation.
Check Multiplication by $2$ : For choice (C), we check if multiplying the original equation by $2$ gives us $-38 = 2 \cdot -25k$ .
Calculation: $-19 \times 2 = -25k \times 2$
$-38 = -50k$
This is equivalent to the original equation because both sides are multiplied by the same factor, $2$ .
Check Multiplication by $-2$ : For choice (D), we check if multiplying $-19$ by $-2$ and $-25k$ by $2$ gives us an equivalent equation. $\newline$ Calculation: $-19 \times (-2) = -25k \times 2$ $\newline$ $38 = 50k$ $\newline$ This is equivalent to the original equation because multiplying both sides by $-2$ is the same as multiplying both sides by $2$ (since $-2 \times -1 = 2$ ).