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

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

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $2$ to the left of $x$ .

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

Add $x$ and $2 x$ .

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

Multiply both sides of the equation by $\frac{2}{3}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{2}{3} \cdot \frac{9}{4}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{1}{3} \cdot \frac{9}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$

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

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