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(6 points )

Answer 1

To solve the equation \( 12 = bY - 3 \) for \( Y \), we can follow these steps:

Step 1: Isolate the term with \( Y \)

Add 3 to both sides of the equation.

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

Justification: This is using the Addition Property of Equality, which states that if two expressions are equal, adding the same value to both sides will maintain the equality.

Step 2: Simplify the left side of the equation

\[ 15 = bY \]

Step 3: Solve for \( Y \) by dividing both sides by \( b \)

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

Justification: This is using the Division Property of Equality, which states that if two expressions are equal, dividing both sides by the same non-zero value will maintain the equality. (We assume \( b \neq 0 \).)

Step 4: Simplify the right side of the equation

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

Final Result

Thus, the solution for \( Y \) in terms of \( b \) is:

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

Summary of Properties Used

1. Addition Property of Equality (Step 1)
2. Division Property of Equality (Step 3)