Solve for b in the following equation: A=12(a+b)

Question

(1 point)
Responses

b=2A−a
b is equal to 2 cap A minus A

b=12A−a
b is equal to 1 half cap A minus A

b=12A+a
b is equal to 1 half cap A plus A

b=2A+a

Answer 1

To solve for \( b \) in the equation \( A = 12(a + b) \), follow these steps:

1. Start with the original equation: \[ A = 12(a + b) \]

2. Divide both sides by 12 to isolate \( a + b \): \[ \frac{A}{12} = a + b \]

3. Subtract \( a \) from both sides to solve for \( b \): \[ b = \frac{A}{12} - a \]

Now, let's express \( \frac{A}{12} \) in terms of \( A \): \[ b = \frac{1}{12}A - a \]

It seems there might have been a misunderstanding with the options given, as they don't directly match the derived formula. However, I see the closest option based on the potential formatting of the outcome could be interpreted as one expressing \( 12A \), but none match exactly.

Please check for proper interpretation or consider if there's a need to convert further or round to fit provided choices. If all were to validate based on typical values present, none are aligned perfectly so ensure replicating properly as some candidates were potentially miswritten, but otherwise, we have:

\( b = \frac{1}{12} A - a\) directly stands for misrepresentation on given choices thus necessitates confirming with problem setter for validation against options provided.