Solve for x 12.25+x=4 1/2

$12.25 + x = 4 \frac{1}{2}$

Simplify the right side.

Convert $4 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$12.25 + x = 4 + \frac{1}{2}$

Add $4$ and $\frac{1}{2}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$12.25 + x = 4 \cdot \frac{2}{2} + \frac{1}{2}$

Combine $4$ and $\frac{2}{2}$ .

$12.25 + x = \frac{4 \cdot 2}{2} + \frac{1}{2}$

Combine the numerators over the common denominator.

$12.25 + x = \frac{4 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $4$ by $2$ .

$12.25 + x = \frac{8 + 1}{2}$

Add $8$ and $1$ .

$12.25 + x = \frac{9}{2}$

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

Subtract $12.25$ from both sides of the equation.

$x = \frac{9}{2} - 12.25$

To write $- 12.25$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{9}{2} - 12.25 \cdot \frac{2}{2}$

Combine $- 12.25$ and $\frac{2}{2}$ .

$x = \frac{9}{2} + \frac{- 12.25 \cdot 2}{2}$

Combine the numerators over the common denominator.

$x = \frac{9 - 12.25 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 12.25$ by $2$ .

$x = \frac{9 - 24.5}{2}$

Subtract $24.5$ from $9$ .

$x = \frac{- 15.5}{2}$

Divide $- 15.5$ by $2$ .

$x = - 7.75$