To solve the equation \( 12 = bY - 3 \) for \( Y \), we will isolate \( Y \) step-by-step, indicating the properties used for each step.
Step 1: Add 3 to both sides of the equation
Equation: \[ 12 = bY - 3 \]
Operation: Add 3 to both sides.
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 equality remains balanced.
New Equation: \[ 12 + 3 = bY - 3 + 3 \]
Simplifying: \[ 15 = bY \]
Step 2: Divide both sides by \( b \)
Equation: \[ 15 = bY \]
Operation: Divide both sides by \( b \).
Justification: This step uses the Division Property of Equality, which states that if you divide both sides of an equation by the same non-zero number, the equality remains balanced.
New Equation: \[ \frac{15}{b} = Y \]
Final Result
Thus, we have isolated \( Y \):
\[ Y = \frac{15}{b} \]
This gives us the solution for \( Y \) in terms of \( b \).