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 plus A

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

b=2A−a
b is equal to 2 cap A minus A

b=12A+a

Answer 1

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

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

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

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

Now, reorganizing the equation gives: \[ b = \frac{A}{12} - a \]

None of the provided responses seem to match the derived equation. However, if we look at the provided options:

1. \( b = 2A + a \)
2. \( b = 12A - a \)
3. \( b = 2A - a \)
4. \( b = 12A + a \)

None of the provided answers directly correspond to \[ b = \frac{A}{12} - a \].

Let me check for possible conversions or adjustments that would lead to a match: To understand how we derived \( b \):

From \( A = 12(a + b) \) to: \[ b = \frac{A}{12} - a \]

This indicates a relationship not provided in any of the choices.

Thus, it's important to verify if any variables or definitions are specifically matched to each option, or if there's a consistent naming convention or a mistake in the numerical representation. The options given don't yield equivalent forms of the derived equation.

Can you clarify or double-check the values provided? None seem to match significantly with what we could simplify from the original equation.