Solve for p 3/4p-2=1/4p+4

$\frac{3}{4} p - 2 = \frac{1}{4} p + 4$

Combine $\frac{3}{4}$ and $p$ .

$\frac{3 p}{4} - 2 = \frac{1}{4} p + 4$

Combine $\frac{1}{4}$ and $p$ .

$\frac{3 p}{4} - 2 = \frac{p}{4} + 4$

Move all terms containing $p$ to the left side of the equation.

Subtract $\frac{p}{4}$ from both sides of the equation.

$\frac{3 p}{4} - 2 - \frac{p}{4} = 4$

Combine the numerators over the common denominator.

$- 2 + \frac{3 p - p}{4} = 4$

Subtract $p$ from $3 p$ .

$- 2 + \frac{2 p}{4} = 4$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 p$ .

$- 2 + \frac{2 (p)}{4} = 4$

Cancel the common factors.

Factor $2$ out of $4$ .

$- 2 + \frac{2 p}{2 \cdot 2} = 4$

Cancel the common factor.

$- 2 + \frac{2 p}{2 \cdot 2} = 4$

Rewrite the expression.

$- 2 + \frac{p}{2} = 4$

Move all terms not containing $p$ to the right side of the equation.

Add $2$ to both sides of the equation.

$\frac{p}{2} = 4 + 2$

Add $4$ and $2$ .

$\frac{p}{2} = 6$

Multiply both sides of the equation by $2$ .

$2 \frac{p}{2} = 2 \cdot 6$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{p}{2} = 2 \cdot 6$

Rewrite the expression.

$p = 2 \cdot 6$

Simplify the right side.

Multiply $2$ by $6$ .

$p = 12$