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Select all of the equations below that are equivalent to:\newlinevw=4vw = -4\newlineUse properties of equality.\newlineMulti-select Choices:\newline(A) vw2=8vw \cdot -2 = 8\newline(B) vw25=100vw \cdot 25 = -100\newline(C) 16vw=48-16vw = 48\newline(D) vw8=32vw \cdot -8 = 32

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Q. Select all of the equations below that are equivalent to:\newlinevw=4vw = -4\newlineUse properties of equality.\newlineMulti-select Choices:\newline(A) vw2=8vw \cdot -2 = 8\newline(B) vw25=100vw \cdot 25 = -100\newline(C) 16vw=48-16vw = 48\newline(D) vw8=32vw \cdot -8 = 32
  1. Identify equation & operation: Identify the original equation and the operation needed to check equivalency. Original equation: vw=4vw = -4. To find equivalent equations, we need to perform valid mathematical operations that maintain equality.
  2. Check option (A): Check option (A): Multiply both sides of vw=4vw = -4 by 2-2. Calculation: (4)×(2)=8(-4) \times (-2) = 8. Compare with (A): vw×2=8vw \times -2 = 8.
  3. Check option (B): Check option (B): Multiply both sides of vw=4vw = -4 by 2525. Calculation: (4)×25=100(-4) \times 25 = -100. Compare with (B): vw×25=100vw \times 25 = -100.
  4. Check option (C): Check option (C): Multiply both sides of vw=4vw = -4 by 4-4, then multiply the result by 44. Calculation: (4)×(4)=16(-4) \times (-4) = 16, 16×4=6416 \times 4 = 64. Compare with (C): 16vw=48-16vw = 48.

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