# Solving One-Step Linear Equations with Mixed Numbers: Subtraction

A
**
mixed number
**
is a number expressed as the sum of a
whole number
and a
fractions
, such as
$3\frac{1}{4}$
.

It is usually easier to do calculations with improper fractions than mixed numbers, but mixed numbers give a better idea of the size of a number. So you should know how to convert back and forth.

To solve an equation that has a mixed number coefficient, we convert the mixed number to an improper fraction as the first step.

Some linear equations can be solved with a single operation. For this type of equation, use the inverse operation to solve. The easiest type involves only an addition or a subtraction.

**
Example:
**

Solve.
*
*

$x-3\frac{1}{2}=\frac{17}{2}$

Rewrite the mixed number as an improper fraction.

$x-\frac{7}{2}=\frac{17}{2}$

The inverse operation of subtraction is addition. Use the addition property of equality to add $\frac{7}{2}$ to both sides.

$x-\frac{7}{2}+\frac{7}{2}=\frac{17}{2}+\frac{7}{2}$

Simplify.

$x=\frac{24}{2}$

Divide the numerator and the denominator by the GCF, $2$ .

$x=12$