Question

solve each equation. use paper or the sketch tool if it helps with your thinking. \\(\frac{3y - 6}{9} = \frac{4 - 2y}{-3}\\)

Explanation:

Step1: Eliminate denominators by cross - multiplying

To solve the equation \(\frac{3y - 6}{9}=\frac{4 - 2y}{-3}\), we cross - multiply. Cross - multiplying gives us \(-3(3y - 6)=9(4 - 2y)\).

Step2: Expand both sides of the equation

First, expand the left - hand side: \(-3\times3y-(-3)\times6=-9y + 18\).
Then, expand the right - hand side: \(9\times4-9\times2y = 36-18y\).
So the equation becomes \(-9y + 18=36-18y\).

Step3: Move the terms with \(y\) to one side and constants to the other side

Add \(18y\) to both sides of the equation: \(-9y+18y + 18=36-18y + 18y\), which simplifies to \(9y + 18=36\).
Subtract 18 from both sides: \(9y+18 - 18=36 - 18\), so \(9y=18\).

Step4: Solve for \(y\)

Divide both sides of the equation \(9y = 18\) by 9: \(y=\frac{18}{9}=2\).

Answer:

\(y = 2\)