Questions: Solve: 3/4 y-6=2+1/4 y y=4 y=8 y=16 y=-8

Solution Steps

To solve the equation \(\frac{3}{4} y - 6 = 2 + \frac{1}{4} y\), we need to isolate the variable \(y\). We can do this by first eliminating the fractions and then solving the resulting linear equation.

1. Subtract \(\frac{1}{4} y\) from both sides to combine the \(y\) terms.
2. Add 6 to both sides to isolate the \(y\) term.
3. Solve for \(y\).

We start with the equation: \[ \frac{3}{4} y - 6 = 2 + \frac{1}{4} y \] To eliminate the fractions, we can rearrange the equation by subtracting \(\frac{1}{4} y\) from both sides: \[ \frac{3}{4} y - \frac{1}{4} y - 6 = 2 \]

This simplifies to: \[ \frac{2}{4} y - 6 = 2 \] or equivalently: \[ \frac{1}{2} y - 6 = 2 \] Next, we add 6 to both sides: \[ \frac{1}{2} y = 8 \]

Now, we multiply both sides by 2 to isolate \(y\): \[ y = 16 \]

Final Answer