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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

3 answers

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

make it original and shorter

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