To solve for \( b \) in the equation \( A = 12(a + b) \), we can follow these steps:
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Start with the equation: \[ A = 12(a + b) \]
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Divide both sides by 12: \[ \frac{A}{12} = a + b \]
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Subtract \( a \) from both sides to isolate \( b \): \[ b = \frac{A}{12} - a \]
Now, we can express it in a more suitable form. However, none of the given options directly reflect this expression.
If we rewrite \( \frac{A}{12} \) as \( \frac{1}{12} A \), we get: \[ b = \frac{1}{12} A - a \]
This expression is not among the options. Therefore, let's re-evaluate the options given that none of the extracted forms seem to match.
It seems that the options might not correspond directly with the derived formula \( b = \frac{A}{12} - a \). If the original values had a constant factor or specific substitutions, please clarify or check the premises of the problem for any additional context or adjustments.
Otherwise, based on the current solution derived from \( A = 12(a + b) \), the option that best reflects the relationship would require a clearer representation of those values.
Let’s analyze the choices provided against our equation:
Given:
- \( b = 2 A - a \)
- \( b = \frac{1}{2} A - a \)
- \( b = 2 A + a \)
- \( b = \frac{1}{2} A + a \)
None are direct equivalents to \( b = \frac{A}{12} - a \). Please check if corrections or reinterpretations of the variables \( A \) and \( a \) yield an appropriate solution context, or let me know if additional information can assist with matching outputs.