Select all of the equations below that are equivalent to: $\newline$ $8 = 9 - r$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $18 = 9 - r + 8$ $\newline$ (B) $16 = 6 + 9 - r$ $\newline$ (C) $20 = 9 - r + 12$ $\newline$ (D) $14 = 6 + 9 - r$

Full solution

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

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8 = 9 - r

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Use properties of equality.

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Multi-select Choices:

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(A)

18 = 9 - r + 8

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(B)

16 = 6 + 9 - r

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(C)

20 = 9 - r + 12

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(D)

14 = 6 + 9 - r

Original Equation: To determine if an equation is equivalent to $8 = 9 - r$ , we can manipulate the original equation using properties of equality and compare it to each choice. $\newline$ Let's start with the original equation: $8 = 9 - r$ .
Choice (A): For choice (A) $18 = 9 - r + 8$ , we can check if it's equivalent by adding $8$ to both sides of the original equation. $\newline$ $8 + 8 = (9 - r) + 8$ $\newline$ $16 = 9 - r + 8$ $\newline$ This does not match choice (A), which has $18$ on the left side instead of $16$ .
Choice (B): For choice (B) $16 = 6 + 9 - r$ , we can check if it's equivalent by adding $6$ to both sides of the original equation. $\newline$ $8 + 6 = (9 - r) + 6$ $\newline$ $14 = 9 - r + 6$ $\newline$ This does not match choice (B), which has $16$ on the left side instead of $14$ .
Choice (C): For choice (C) $20 = 9 - r + 12$ , we can check if it's equivalent by adding $12$ to both sides of the original equation. $\newline$ $8 + 12 = (9 - r) + 12$ $\newline$ $20 = 9 - r + 12$ $\newline$ This matches choice (C), so it is equivalent to the original equation.
Choice (D): For choice (D) $14 = 6 + 9 - r$ , we can check if it's equivalent by adding $6$ to both sides of the original equation. $\newline$ $8 + 6 = (9 - r) + 6$ $\newline$ $14 = 9 - r + 6$ $\newline$ This matches choice (D), so it is equivalent to the original equation.