Solve the equation: 12 = bY - 3 for Y. Show each step used to solve for Y and justify by giving the property used for each step.

Answer 1

To solve the equation \( 12 = bY - 3 \) for \( Y \), we will isolate \( Y \) by following these steps:

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 (or subtract) the same amount 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 Division Property of Equality, which states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.

Result:
\[ Y = \frac{15}{b} \]

Conclusion

Thus, the solution to the equation \( 12 = bY - 3 \) for \( Y \) is:
\[ Y = \frac{15}{b} \]