Select all of the equations below that are equivalent to: $\newline$ $9n = 14$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $9n − 3 = 11$ $\newline$ (B) $9n − 7 = 7$ $\newline$ (C) $9n − 2 = 12$ $\newline$ (D) $9n − 10 = 4$

Full solution

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

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9n = 14

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Use properties of equality.

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Multi-select Choices:

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(A)

9n  −  3 = 11

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(B)

9n  −  7 = 7

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(C)

9n  −  2 = 12

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(D)

9n  −  10 = 4

Manipulate Original Equation: To determine if an equation is equivalent to $9n = 14$ , we can manipulate the original equation using properties of equality and compare it to each choice.
Check Choice (A): Let's start with choice (A): $9n - 3 = 11$ . We can add $3$ to both sides of the original equation ( $9n = 14$ ) to see if it matches choice (A). $9n + 3 = 14 + 3$ $9n + 3 = 17$ This does not match choice (A), which states $9n - 3 = 11$ .
Check Choice (B): Now let's check choice (B): $9n − 7 = 7$ . We can add $7$ to both sides of the original equation ( $9n = 14$ ) to see if it matches choice (B). $9n + 7 = 14 + 7$ $9n + 7 = 21$ This does not match choice (B), which states $9n − 7 = 7$ .
Check Choice (C): Next, we examine choice (C): $9n - 2 = 12$ . We can add $2$ to both sides of the original equation ( $9n = 14$ ) to see if it matches choice (C). $9n + 2 = 14 + 2$ $9n + 2 = 16$ This does not match choice (C), which states $9n - 2 = 12$ .
Check Choice (D): Finally, let's look at choice (D): $9n - 10 = 4$ . We can add $10$ to both sides of the original equation ( $9n = 14$ ) to see if it matches choice (D). $9n + 10 = 14 + 10$ $9n + 10 = 24$ This does not match choice (D), which states $9n - 10 = 4$ .