Select all of the equations below that are equivalent to: $\newline$ $m + n = 15$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $5 + m + n = 20$ $\newline$ (B) $m + n + 4 = 20$ $\newline$ (C) $3 + m + n = 16$ $\newline$ (D) $2 + m + n = 18$

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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

m + n = 15

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

5 + m + n = 20

\newline

(B)

m + n + 4 = 20

\newline

(C)

3 + m + n = 16

\newline

(D)

2 + m + n = 18

Given Equation Analysis: We are given the equation $m + n = 15$ . To determine which of the choices are equivalent, we can add the same value to both sides of the given equation and see if it matches any of the choices.
Checking Choice (A): Let's start with choice (A): $5 + m + n = 20$ . To check if it's equivalent, we add $5$ to both sides of the original equation: $m + n + 5 = 15 + 5$ .
Checking Choice (B): After performing the addition, we get $m + n + 5 = 20$ . This matches choice (A), so (A) is equivalent to the original equation.
Checking Choice (C): Now let's check choice (B): $m + n + 4 = 20$ . We add $4$ to both sides of the original equation: $m + n + 4 = 15 + 4$ .
Checking Choice (D): After performing the addition, we get $m + n + 4 = 19$ . This does not match choice (B), so (B) is not equivalent to the original equation.
Checking Choice (D): After performing the addition, we get $m + n + 4 = 19$ . This does not match choice (B), so (B) is not equivalent to the original equation.Next, we check choice (C): $3 + m + n = 16$ . We add $3$ to both sides of the original equation: $m + n + 3 = 15 + 3$ .
Checking Choice (D): After performing the addition, we get $m + n + 4 = 19$ . This does not match choice (B), so (B) is not equivalent to the original equation.Next, we check choice (C): $3 + m + n = 16$ . We add $3$ to both sides of the original equation: $m + n + 3 = 15 + 3$ .After performing the addition, we get $m + n + 3 = 18$ . This does not match choice (C), so (C) is not equivalent to the original equation.
Checking Choice (D): After performing the addition, we get $m + n + 4 = 19$ . This does not match choice (B), so (B) is not equivalent to the original equation.Next, we check choice (C): $3 + m + n = 16$ . We add $3$ to both sides of the original equation: $m + n + 3 = 15 + 3$ .After performing the addition, we get $m + n + 3 = 18$ . This does not match choice (C), so (C) is not equivalent to the original equation.Finally, we check choice (D): $2 + m + n = 18$ . We add $2$ to both sides of the original equation: $m + n + 2 = 15 + 2$ .
Checking Choice (D): After performing the addition, we get $m + n + 4 = 19$ . This does not match choice (B), so (B) is not equivalent to the original equation.Next, we check choice (C): $3 + m + n = 16$ . We add $3$ to both sides of the original equation: $m + n + 3 = 15 + 3$ .After performing the addition, we get $m + n + 3 = 18$ . This does not match choice (C), so (C) is not equivalent to the original equation.Finally, we check choice (D): $2 + m + n = 18$ . We add $2$ to both sides of the original equation: $m + n + 2 = 15 + 2$ .After performing the addition, we get $m + n + 2 = 17$ . This does not match choice (D), so (D) is not equivalent to the original equation.