Question

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.