Solve for x x/3-1/2=3/4

$\frac{x}{3} - \frac{1}{2} = \frac{3}{4}$

Step 1

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

Add $\frac{1}{2}$ to both sides of the equation.

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

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

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

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

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

$\frac{x}{3} = \frac{3}{4} + \frac{2}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{x}{3} = \frac{3}{4} + \frac{2}{4}$

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{3 + 2}{4}$

Add $3$ and $2$ .

$\frac{x}{3} = \frac{5}{4}$

Step 2

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 (\frac{5}{4})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 (\frac{5}{4})$

Rewrite the expression.

$x = 3 (\frac{5}{4})$

Simplify the right side.

Multiply $3 (\frac{5}{4})$ .

Combine $3$ and $\frac{5}{4}$ .

$x = \frac{3 \cdot 5}{4}$

Multiply $3$ by $5$ .

$x = \frac{15}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{4}$

Decimal Form:

$x = 3.75$

Mixed Number Form:

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