Question

if $a\div4 = 11$, does $a\div4 + 4 = 11 + 4$? explain.

choose the correct answer below.

a. no. the second equation is not exactly the same as the first equation, so it cannot be true.

b. no. a different number was added to each side of the equation.

c. yes. both equations have $a\div4$ on the left side and 11 on the right side.

d. yes. the same number was added to each side of the equation.

Explanation:

To determine if \( a\div4 + 4=11 + 4\) is true given \( a\div4 = 11\), we use the Addition Property of Equality. This property states that if we add the same number to both sides of an equation, the equation remains true. Here, we add 4 to both sides of \( a\div4=11\):

• Left side: \( a\div4+4\) (adding 4 to \( a\div4\))
• Right side: \( 11 + 4\) (adding 4 to 11)

Since we added the same number (4) to both sides of the original equation, the new equation is true.

Now let's analyze the options:

• Option A: Incorrect. The Addition Property of Equality allows us to add the same number to both sides, so the second equation can be true even if it's not identical to the first.
• Option B: Incorrect. We added the same number (4) to both sides, not different numbers.
• Option C: Incorrect. The reasoning is not about having \( a\div4\) on the left and 11 on the right, but about the Addition Property of Equality.
• Option D: Correct. We applied the Addition Property of Equality by adding 4 to both sides.

Answer:

D. Yes. The same number was added to each side of the equation.