Select all of the equations below that are equivalent to: $\newline$ $7 - n = 13$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $7 - n - 2 = 11$ $\newline$ (B) $7 - n - 3 = 10$ $\newline$ (C) $7 - n - 11 = 2$ $\newline$ (D) $7 - n - 10 = 3$

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Algebra 1

Identify equivalent equations

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

\newline

7 - n = 13

\newline

Use properties of equality.

\newline

\newline

Multi-select Choices:

\newline

(A)

7 - n - 2 = 11

\newline

(B)

7 - n - 3 = 10

\newline

(C)

7 - n - 11 = 2

\newline

(D)

7 - n - 10 = 3

Manipulate Original Equation: To determine if the equations are equivalent, we can manipulate the original equation $7 - n = 13$ using properties of equality to see if we can transform it into any of the given choices.
Check Choice (A): First, let's look at choice (A): $7 - n - 2 = 11$ . We can start with the original equation and subtract $2$ from both sides to see if we get the equation in choice (A). $\newline$ $7 - n = 13$ $\newline$ Subtract $2$ from both sides: $\newline$ $(7 - n) - 2 = 13 - 2$ $\newline$ $7 - n - 2 = 11$ $\newline$ This matches choice (A), so (A) is equivalent to the original equation.
Check Choice (B): Now, let's look at choice (B): $7 - n - 3 = 10$ . We can start with the original equation and subtract $3$ from both sides to see if we get the equation in choice (B). $\newline$ $7 - n = 13$ $\newline$ Subtract $3$ from both sides: $\newline$ $(7 - n) - 3 = 13 - 3$ $\newline$ $7 - n - 3 = 10$ $\newline$ This matches choice (B), so (B) is equivalent to the original equation.
Check Choice (C): Next, let's look at choice (C): $7 − n − 11 = 2$ . We can start with the original equation and subtract $11$ from both sides to see if we get the equation in choice (C). $\newline$ $7 − n = 13$ $\newline$ Subtract $11$ from both sides: $\newline$ $(7 − n) − 11 = 13 − 11$ $\newline$ $7 − n − 11 = 2$ $\newline$ This matches choice (C), so (C) is equivalent to the original equation.
Check Choice (D): Finally, let's look at choice (D): $7 − n − 10 = 3$ . We can start with the original equation and subtract $10$ from both sides to see if we get the equation in choice (D). $\newline$ $7 − n = 13$ $\newline$ Subtract $10$ from both sides: $\newline$ $(7 − n) − 10 = 13 − 10$ $\newline$ $7 − n − 10 = 3$ $\newline$ This matches choice (D), so (D) is equivalent to the original equation.