Questions: 6(y-2)-3y=4(y+3)

Solution Steps

To solve the equation \(6(y-2) - 3y = 4(y+3)\), we will first expand both sides to eliminate the parentheses. Then, we will combine like terms and isolate the variable \(y\) on one side of the equation to solve for it.

Start by expanding both sides of the equation \(6(y-2) - 3y = 4(y+3)\).

\[ 6(y-2) = 6y - 12 \] \[ 4(y+3) = 4y + 12 \]

Substituting these into the equation gives:

\[ 6y - 12 - 3y = 4y + 12 \]

Combine like terms on the left side of the equation:

\[ 3y - 12 = 4y + 12 \]

To isolate \(y\), subtract \(4y\) from both sides:

\[ 3y - 4y - 12 = 12 \]

This simplifies to:

\[ -y - 12 = 12 \]

Add 12 to both sides to further isolate \(y\):

\[ -y = 24 \]

Multiply both sides by \(-1\) to solve for \(y\):

\[ y = -24 \]

Final Answer