Select all of the equations below that are equivalent to: w + –5 = 28 Use properties of equality. Multi-select Choices: (A)–3(w + –5) = –84 (B)–16w + 80 = –16 · 28 (C)7w + –35 = 7 · 28 (D)2(w + –5) = 56

Question

Select all of the equations below that are equivalent to:  w + –5 = 28 Use properties of equality.    Multi-select Choices: (A)–3(w  +  –5) = –84 (B)–16w  +  80 = –16  ·  28 (C)7w  +  –35 = 7  ·  28 (D)2(w  +  –5) = 56

Bytelearn · Accepted Answer

Identify Original Equation: First, let's identify the original equation we are comparing to: w + (–5) = 28 We need to determine which of the choices are equivalent to this equation by using properties of equality.Check Option (A): Let's check option (A): (A) –3(w + –5) = –84 We can distribute the –3 to both w and –5: –3w + 15 = –84 This is not equivalent to the original equation because if we divide both sides by –3 to reverse the operation, we do not get the original equation.Check Option (B): Let's check option (B): (B) –16w + 80 = –16 · 28 First, calculate –16 · 28: –16 · 28 = –448 Now the equation is: –16w + 80 = –448 This is not equivalent to the original equation because if we add 16w to both sides and then subtract 80 from both sides, we do not get the original equation.Check Option (C): Let's check option (C): (C) 7w + –35 = 7 · 28 First, calculate 7 · 28: 7 · 28 = 196 Now the equation is: 7w – 35 = 196 This is equivalent to the original equation because if we divide both sides by 7 to reverse the operation, we get the original equation: w – 5 = 28Check Option (D): Let's check option (D): (D) 2(w + –5) = 56 We can distribute the 2 to both w and –5: 2w – 10 = 56 This is equivalent to the original equation because if we divide both sides by 2 to reverse the operation, we get the original equation: w – 5 = 28

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