Select all of the equations below that are equivalent to: $\newline$ $27 = wx$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $-54 = wx \cdot -2$ $\newline$ (B) $75 = 3wx$ $\newline$ (C) $-81 = -3wx$ $\newline$ (D) $81 = wx \cdot 3$

Full solution

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

\newline

27 = wx

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

-54 = wx \cdot -2

\newline

(B)

75 = 3wx

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(C)

-81 = -3wx

\newline

(D)

81 = wx \cdot 3

Identify Equation: Identify the original equation and understand the task. $\newline$ The original equation is $27 = wx$ , and we need to find which of the given choices are equivalent to this equation by using properties of equality.
Analyze Choice (A): Analyze choice (A) $–54 = wx \cdot –2$ . To determine if this is equivalent to $27 = wx$ , we can simplify the right side by dividing both sides by $–2$ . $–54 / –2 = (wx \cdot –2) / –2$ $27 = wx$ This shows that choice (A) is equivalent to the original equation.
Analyze Choice (B): Analyze choice (B) $75 = 3wx$ . To determine if this is equivalent to $27 = wx$ , we can simplify the right side by dividing both sides by $3$ . $\frac{75}{3} = \frac{3wx}{3}$ $25 = wx$ This shows that choice (B) is not equivalent to the original equation.
Analyze Choice (C): Analyze choice (C) $–81 = –3wx$ . To determine if this is equivalent to $27 = wx$ , we can simplify the right side by dividing both sides by $–3$ . $–81 / –3 = (–3wx) / –3$ $27 = wx$ This shows that choice (C) is equivalent to the original equation.
Analyze Choice (D): Analyze choice (D) $81 = wx \cdot 3$ . To determine if this is equivalent to $27 = wx$ , we can simplify the right side by dividing both sides by $3$ . $\frac{81}{3} = \frac{(wx \cdot 3)}{3}$ $27 = wx$ This shows that choice (D) is equivalent to the original equation.