Solve for x 3/4x+3/2x=9/4

$\frac{3}{4} x + \frac{3}{2} x = \frac{9}{4}$

Simplify $\frac{3}{4} x + \frac{3}{2} x$ .

Simplify each term.

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

$\frac{3 x}{4} + \frac{3}{2} x = \frac{9}{4}$

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{4} + \frac{3 x}{2} = \frac{9}{4}$

To write $\frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{4} + \frac{3 x}{2} \cdot \frac{2}{2} = \frac{9}{4}$

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

Multiply $\frac{3 x}{2}$ by $\frac{2}{2}$ .

$\frac{3 x}{4} + \frac{3 x \cdot 2}{2 \cdot 2} = \frac{9}{4}$

Multiply $2$ by $2$ .

$\frac{3 x}{4} + \frac{3 x \cdot 2}{4} = \frac{9}{4}$

Combine the numerators over the common denominator.

$\frac{3 x + 3 x \cdot 2}{4} = \frac{9}{4}$

Simplify the numerator.

Factor $3 x$ out of $3 x + 3 x \cdot 2$ .

Factor $3 x$ out of $3 x$ .

$\frac{3 x (1) + 3 x \cdot 2}{4} = \frac{9}{4}$

Factor $3 x$ out of $3 x \cdot 2$ .

$\frac{3 x (1) + 3 x (2)}{4} = \frac{9}{4}$

Factor $3 x$ out of $3 x (1) + 3 x (2)$ .

$\frac{3 x (1 + 2)}{4} = \frac{9}{4}$

Add $1$ and $2$ .

$\frac{3 x \cdot 3}{4} = \frac{9}{4}$

Multiply $3$ by $3$ .

$\frac{9 x}{4} = \frac{9}{4}$

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

$9 x = 9$

Divide each term in $9 x = 9$ by $9$ and simplify.

Divide each term in $9 x = 9$ by $9$ .

$\frac{9 x}{9} = \frac{9}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{9}{9}$

Divide $x$ by $1$ .

$x = \frac{9}{9}$

Simplify the right side.

Divide $9$ by $9$ .

$x = 1$