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Select all of the equations below that are equivalent to:\newlinepq=98pq = 98\newlineUse properties of equality.\newlineMulti-select Choices:\newline(A)pq2=49\frac{pq}{-2} = -49\newline(B)pq7=14\frac{pq}{-7} = -14\newline(C)pq2=49\frac{pq}{2} = 49\newline(D)pq14=7\frac{pq}{14} = 7

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Q. Select all of the equations below that are equivalent to:\newlinepq=98pq = 98\newlineUse properties of equality.\newlineMulti-select Choices:\newline(A)pq2=49\frac{pq}{-2} = -49\newline(B)pq7=14\frac{pq}{-7} = -14\newline(C)pq2=49\frac{pq}{2} = 49\newline(D)pq14=7\frac{pq}{14} = 7
  1. Divide by 2-2: To determine if an equation is equivalent to pq=98pq = 98, we can perform the same operation on both sides of the original equation and see if we get the equation in question.\newlineLet's start with option (A): pq2=49\frac{pq}{-2} = -49.\newlineWe divide both sides of the original equation pq=98pq = 98 by 2-2.\newlinepq2=982\frac{pq}{-2} = \frac{98}{-2}\newlinepq2=49\frac{pq}{-2} = -49\newlineThis matches option (A), so it is equivalent.
  2. Divide by 7-7: Now let's check option (B): pq/(7)=14pq/(-7) = -14. We divide both sides of the original equation pq=98pq = 98 by 7-7. pq/(7)=98/(7)pq/(-7) = 98/(-7) pq/(7)=14pq/(-7) = -14 This matches option (B), so it is equivalent.
  3. Divide by 22: Next, we check option (C): pq/2=49pq/2 = 49. We divide both sides of the original equation pq=98pq = 98 by 22. pq/2=98/2pq/2 = 98/2 pq/2=49pq/2 = 49 This matches option (C), so it is equivalent.
  4. Divide by 1414: Finally, we check option (D): pq/14=7pq/14 = 7. We divide both sides of the original equation pq=98pq = 98 by 1414. pq/14=98/14pq/14 = 98/14 pq/14=7pq/14 = 7 This matches option (D), so it is equivalent.

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