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

Question

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

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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.

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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