Select all of the equations below that are equivalent to: –21 = 4r Use properties of equality. Multi-select Choices: (A)–22 · –21 = –88r (B)–23 · –21 = –92r (C)42 = 4r · –2 (D)–84 = 4r · 4

Question

Select all of the equations below that are equivalent to:  –21 = 4r Use properties of equality.    Multi-select Choices: (A)–22  ·  –21 = –88r (B)–23  ·  –21 = –92r (C)42 = 4r  ·  –2 (D)–84 = 4r  ·  4

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Check Equivalence Operation: Which operation should be used to check if the equations are equivalent? To check if the equations are equivalent, we need to see if the operations performed on both sides of the original equation maintain equality.Check Equation (A): Check equation (A) –22 · –21 = –88r. To see if this equation is equivalent to –21 = 4r, we need to simplify the left side and see if the right side has been multiplied by the same factor. –22 · –21 = 462 (since multiplying two negatives gives a positive) This does not match the original equation because the left side of the original equation is –21, not 462.Check Equation (B): Check equation (B) –23 · –21 = –92r. To see if this equation is equivalent to –21 = 4r, we need to simplify the left side and see if the right side has been multiplied by the same factor. –23 · –21 = 483 (since multiplying two negatives gives a positive) This does not match the original equation because the left side of the original equation is –21, not 483.Check Equation (C): Check equation (C) 42 = 4r · –2. To see if this equation is equivalent to –21 = 4r, we need to simplify the right side and see if it matches the left side when the same operation is applied. 4r · –2 = –8r This does not match the original equation because the right side of the original equation is 4r, not –8r.Check Equation (D): Check equation (D) –84 = 4r · 4. To see if this equation is equivalent to –21 = 4r, we need to simplify the right side and see if it matches the left side when the same operation is applied. 4r · 4 = 16r This does not match the original equation because the right side of the original equation is 4r, not 16r.

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