To solve the equation \( 12 = bY - 3 \) for \( Y \), we will isolate \( Y \) step by step, justifying each step with the appropriate property.
Step 1: Add 3 to both sides
Equation:
\[ 12 + 3 = bY - 3 + 3 \]
Justification:
This step uses the Addition Property of Equality, which states that if you add the same number to both sides of an equation, the two sides remain equal.
Result:
\[ 15 = bY \]
Step 2: Divide both sides by \( b \)
Equation:
\[ \frac{15}{b} = \frac{bY}{b} \]
Justification:
This step uses the Multiplicative Property of Equality, which states that if you divide both sides of an equation by the same nonzero number, the two sides are still equal. (Note: We assume \( b \neq 0 \) to avoid division by zero.)
Result:
\[ Y = \frac{15}{b} \]
Final Result
The solution to the equation \( 12 = bY - 3 \) for \( Y \) is: \[ Y = \frac{15}{b} \]
This shows each step used to solve for \( Y \) with justifications provided for the properties applied.