Select all of the equations below that are equivalent to: 13 + v = –11 Use properties of equality. Multi-select Choices: (A)39 + 3v = 3 · –11 (B)3(13 + v) = –33 (C)–28 + –2v = –2 · –11 (D)–52 + –4v = –4 · –11

Question

Select all of the equations below that are equivalent to:  13 + v = –11 Use properties of equality.    Multi-select Choices: (A)39  +  3v = 3  ·  –11 (B)3(13  +  v) = –33 (C)–28  +  –2v = –2  ·  –11 (D)–52  +  –4v = –4  ·  –11

Bytelearn · Accepted Answer

Apply Distributive Property: To determine if an equation is equivalent to 13 + v = –11, we can apply the distributive property and simplify each choice to see if it matches the original equation.Check Choice (A): For choice (A) 39 + 3v = 3 · –11, we apply the distributive property to the right side: 3 · –11 = –33 So, the equation becomes 39 + 3v = –33. Now, we divide each term by 3 to see if it simplifies to the original equation: (39 + 3v) / 3 = –33 / 3 13 + v = –11 This matches the original equation, so (A) is equivalent.Check Choice (B): For choice (B) 3(13 + v) = –33, we apply the distributive property to the left side: 3 * 13 + 3v = –33 39 + 3v = –33 This is the same as choice (A), which we already determined to be equivalent. So, (B) is also equivalent.Check Choice (C): For choice (C) –28 + –2v = –2 · –11, we apply the distributive property to the right side: –2 · –11 = 22 So, the equation becomes –28 + –2v = 22. Now, we add 28 to both sides to see if it simplifies to the original equation: –28 + 28 + –2v = 22 + 28 –2v = 50 This does not match the original equation, so (C) is not equivalent.Check Choice (D): For choice (D) –52 + –4v = –4 · –11, we apply the distributive property to the right side: –4 · –11 = 44 So, the equation becomes –52 + –4v = 44. Now, we add 52 to both sides to see if it simplifies to the original equation: –52 + 52 + –4v = 44 + 52 –4v = 96 This does not match the original equation, so (D) is not equivalent.

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