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 \( Y \) step by step. Here are the steps along with the justifications for each:

Step 1: Add 3 to both sides of the 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 of the equation by \( b \), assuming \( b \neq 0 \).

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

Justification:

This step uses the Division Property of Equality, which states that you can divide both sides of an equation by the same nonzero number.

Result:

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

Final Result:

The solution to the equation is: \[ Y = \frac{15}{b} \]

These steps clearly outline how to isolate \( Y \) and the properties used at each stage to maintain equality.