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Select all of the equations below that are equivalent to:\newlineq+5=21q + -5 = -21\newlineUse properties of equality.\newlineMulti-select Choices:\newline(A) 15q+75=1521-15q + 75 = -15 \cdot -21\newline(B) 5q+25=521-5q + 25 = -5 \cdot -21\newline(C) 2q+10=221-2q + 10 = -2 \cdot -21\newline(D) (q+5)4=84(q + -5) \cdot -4 = 84

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Q. Select all of the equations below that are equivalent to:\newlineq+5=21q + -5 = -21\newlineUse properties of equality.\newlineMulti-select Choices:\newline(A) 15q+75=1521-15q + 75 = -15 \cdot -21\newline(B) 5q+25=521-5q + 25 = -5 \cdot -21\newline(C) 2q+10=221-2q + 10 = -2 \cdot -21\newline(D) (q+5)4=84(q + -5) \cdot -4 = 84
  1. Given Equation Analysis: We are given the equation q+(5)=21q + (-5) = -21. To determine if the other equations are equivalent, we need to apply properties of equality to transform the given equation and compare it with each choice.
  2. Choice (A) Evaluation: Let's start with choice (A): 15q+75=1521-15q + 75 = -15 \cdot -21. We can apply the distributive property to the right side of the equation to see if it simplifies to q+5=21q + -5 = -21.\newlineDistribute 15-15 to 21-21: 15×21=315-15 \times -21 = 315.\newlineNow the equation is 15q+75=315-15q + 75 = 315. To check if it's equivalent, we need to divide all terms by 15-15 to see if we get q+5=21q + -5 = -21.\newlineDivide by 15-15: q=5q = -5, which is not the same as q+5=21q + -5 = -21.

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