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. Please.

Answer 1

To solve the equation \( 12 = bY - 3 \) for \( Y \), we will perform the following steps, identifying the properties used in each step.

1. Add 3 to both sides of the equation.

   \[ 12 + 3 = bY - 3 + 3 \]

   Using the Addition Property of Equality, we maintain the equality by adding the same value (3) to both sides.

   \[ 15 = bY \]

2. Now, divide both sides by \( b \) to isolate \( Y \).

   \[ \frac{15}{b} = \frac{bY}{b} \]

   Using the Division Property of Equality, we maintain the equality by dividing both sides by the same non-zero number (assuming \( b \neq 0 \)).

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

3. Rearranging, we write the solution.

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

Thus, the solution for \( Y \) is:

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

In summary, we used the Addition Property of Equality in step 1 and the Division Property of Equality in step 2 to isolate \( Y \).