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.





make it really short and simple

Answer 1

make it original and shorter

Answer 2

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

1. **Add 3 to both sides**:
\[
12 + 3 = bY - 3 + 3
\]
**Property Used**: Addition Property of Equality.
This simplifies to:
\[
15 = bY
\]

2. **Divide both sides by \( b \)**:
\[
\frac{15}{b} = \frac{bY}{b}
\]
**Property Used**: Division Property of Equality.
This simplifies to:
\[
Y = \frac{15}{b}
\]

Thus, the solution is:
\[
Y = \frac{15}{b}
\]

Answer 3

To solve \( 12 = bY - 3 \) for \( Y \):

1. **Add 3**:
\[
12 + 3 = bY \quad \text{(Addition Property)}
\]
This simplifies to:
\[
15 = bY
\]

2. **Divide by \( b \)**:
\[
Y = \frac{15}{b} \quad \text{(Division Property)}
\]

Final answer:
\[
Y = \frac{15}{b}
\]