Select all of the equations below that are equivalent to: z + 2 = 7 Use properties of equality. Multi-select Choices: (A)–33z + –99 = –33 · 7 (B)2z + 6 = 2 · 7 (C)32z + 64 = 32 · 7 (D)–23z + –92 = –23 · 7

Question

Select all of the equations below that are equivalent to:  z + 2 = 7 Use properties of equality.    Multi-select Choices: (A)–33z  +  –99 = –33  ·  7 (B)2z  +  6 = 2  ·  7 (C)32z  +  64 = 32  ·  7 (D)–23z  +  –92 = –23  ·  7

Bytelearn · Accepted Answer

Check Equation (A): To determine if the equations are equivalent, we need to check if they can be simplified or transformed into the form z + 2 = 7 by using properties of equality, such as multiplication or division by the same non-zero number on both sides of the equation.Check Equation (B): Let's start with option (A): –33z + –99 = –33 · 7 We can simplify this by dividing both sides by –33 to see if we get the original equation. –33z / –33 + –99 / –33 = –33 · 7 / –33 z + 3 = 7 This is not equivalent to z + 2 = 7 because the constant term is different.Check Equation (C): Now let's check option (B): 2z + 6 = 2 · 7 Divide both sides by 2 to see if it simplifies to the original equation. 2z / 2 + 6 / 2 = 2 · 7 / 2 z + 3 = 7 This is also not equivalent to z + 2 = 7 because the constant term is different.Check Equation (D): Next, let's examine option (C): 32z + 64 = 32 · 7 Divide both sides by 32 to check for equivalence. 32z / 32 + 64 / 32 = 32 · 7 / 32 z + 2 = 7 This is equivalent to the original equation z + 2 = 7.Finally, let's look at option (D): –23z + –92 = –23 · 7 Divide both sides by –23 to check for equivalence. –23z / –23 + –92 / –23 = –23 · 7 / –23 z + 4 = 7 This is not equivalent to z + 2 = 7 because the constant term is different.

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