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

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

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

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

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

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{3 a}{4} = \frac{1}{2} + \frac{1}{4}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 a}{4} = \frac{1}{2} \cdot \frac{2}{2} + \frac{1}{4}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{3 a}{4} = \frac{2}{2 \cdot 2} + \frac{1}{4}$

Multiply $2$ by $2$ .

$\frac{3 a}{4} = \frac{2}{4} + \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{3 a}{4} = \frac{2 + 1}{4}$

Add $2$ and $1$ .

$\frac{3 a}{4} = \frac{3}{4}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 a = 3$

Divide each term in $3 a = 3$ by $3$ and simplify.

Divide each term in $3 a = 3$ by $3$ .

$\frac{3 a}{3} = \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} = \frac{3}{3}$

Divide $a$ by $1$ .

$a = \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$a = 1$