Select all of the equations below that are equivalent to: $\newline$ $12 = xy$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $2 = xy - 9$ $\newline$ (B) $7 = xy - 5$ $\newline$ (C) $4 = xy - 8$ $\newline$ (D) $2 = xy - 10$

Full solution

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

\newline

12 = xy

\newline

Use properties of equality.

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Multi-select Choices:

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(A)

2 = xy - 9

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(B)

7 = xy - 5

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(C)

4 = xy - 8

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(D)

2 = xy - 10

Original Equation: To determine if an equation is equivalent to $12 = xy$ , we can manipulate the original equation and compare it to the choices given. We start with the original equation: $\newline$ $12 = xy$ $\newline$ Which operation should be used to compare with the choices? $\newline$ We should subtract a value from both sides of the equation to match the format of the choices.
Comparison with Choice (A): Let's compare the original equation with choice (A): $\newline$ $12 = xy$ $\newline$ Subtract $9$ from both sides: $\newline$ $12 - 9 = xy - 9$ $\newline$ $3 = xy - 9$ $\newline$ This does not match choice (A), which states $2 = xy - 9$ .
Comparison with Choice (B): Now let's compare the original equation with choice (B): $\newline$ $12 = xy$ $\newline$ Subtract $5$ from both sides: $\newline$ $12 - 5 = xy - 5$ $\newline$ $7 = xy - 5$ $\newline$ This matches choice (B), which states $7 = xy - 5$ .
Comparison with Choice (C): Next, let's compare the original equation with choice (C):
$12 = xy$
Subtract $8$ from both sides:
$12 - 8 = xy - 8$
$4 = xy - 8$
This matches choice (C), which states $4 = xy - 8$ .
Comparison with Choice (D): Finally, let's compare the original equation with choice (D):
$12 = xy$
Subtract $10$ from both sides:
$12 - 10 = xy - 10$
$2 = xy - 10$
This does not match choice (D), which states $2 = xy - 10$ .