Select all of the equations below that are equivalent to: –10 = –32 − v Use properties of equality. Multi-select Choices: (A)3 · –10 = –96 − 3v (B)2 · –10 = –64 − 2v (C)–2 · –10 = 64 − –2v (D)–100 = (–32 − v) · 10

Question

Select all of the equations below that are equivalent to:  –10 = –32 − v Use properties of equality.    Multi-select Choices: (A)3  ·  –10 = –96  −  3v (B)2  ·  –10 = –64  −  2v (C)–2  ·  –10 = 64  −  –2v (D)–100 = (–32  −  v)  ·  10

Bytelearn · Accepted Answer

Check Equivalence: To determine if the equations are equivalent, we need to check if the operations applied to both sides of the original equation are valid and maintain equality. Let's start with option (A): (A) 3 · –10 = –96 − 3v We need to check if multiplying both sides of the original equation by 3 gives us this result.Option (A): Multiply both sides of the original equation by 3: 3 * (–10) = 3 * (–32 − v) –30 = –96 − 3v This matches option (A), so (A) is equivalent.Option (B): Now let's check option (B): (B) 2 · –10 = –64 − 2v We need to check if multiplying both sides of the original equation by 2 gives us this result.Option (C: Multiply both sides of the original equation by 2: 2 * (–10) = 2 * (–32 − v) –20 = –64 − 2v This matches option (B), so (B) is equivalent.Next, let's check option (C): (C) –2 · –10 = 64 − (–2v) We need to check if multiplying both sides of the original equation by –2 gives us this result.Multiply both sides of the original equation by –2: –2 * (–10) = –2 * (–32 − v) 20 = 64 + 2v This does not match option (C) because the sign in front of 2v should be positive, not negative.

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