Select all of the equations below that are equivalent to: $\newline$ $10 = 5 + r$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $20 = 9 + 5 + r$ $\newline$ (B) $14 = 4 + 5 + r$ $\newline$ (C) $13 = 3 + 5 + r$ $\newline$ (D) $14 = 3 + 5 + r$

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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

10 = 5 + r

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

20 = 9 + 5 + r

\newline

(B)

14 = 4 + 5 + r

\newline

(C)

13 = 3 + 5 + r

\newline

(D)

14 = 3 + 5 + r

Original Equation: We start with the original equation: $10 = 5 + r$ . To determine if the other equations are equivalent, we need to see if they simplify to the same form.
Choice (A): Let's examine choice (A) $20 = 9 + 5 + r$ . We can simplify the right side by adding $9 + 5$ to get $14 + r$ . So, the equation becomes $20 = 14 + r$ . To check if it's equivalent to $10 = 5 + r$ , we can subtract $14$ from both sides to see if we get the original equation. $20 - 14 = 14 + r - 14$ , which simplifies to $6 = r$ . This does not match the original equation, so (A) is not equivalent.
Choice (B): Now let's look at choice (B) $14 = 4 + 5 + r$ . We can simplify the right side by adding $4 + 5$ to get $9 + r$ . So, the equation becomes $14 = 9 + r$ . To check if it's equivalent to $10 = 5 + r$ , we can subtract $9$ from both sides to see if we get the original equation. $14 - 9 = 9 + r - 9$ , which simplifies to $5 = r$ . This does not match the original equation, so (B) is not equivalent.
Choice (C): Next, we consider choice (C) $13 = 3 + 5 + r$ . We can simplify the right side by adding $3 + 5$ to get $8 + r$ . So, the equation becomes $13 = 8 + r$ . To check if it's equivalent to $10 = 5 + r$ , we can subtract $8$ from both sides to see if we get the original equation. $13 - 8 = 8 + r - 8$ , which simplifies to $5 = r$ . This matches the original equation, so (C) is equivalent.
Choice (D): Finally, we examine choice (D) $14 = 3 + 5 + r$ . We can simplify the right side by adding $3 + 5$ to get $8 + r$ . So, the equation becomes $14 = 8 + r$ . To check if it's equivalent to $10 = 5 + r$ , we can subtract $8$ from both sides to see if we get the original equation. $14 - 8 = 8 + r - 8$ , which simplifies to $6 = r$ . This does not match the original equation, so (D) is not equivalent.