# Solving One–Step Linear Equations with Mixed Numbers

A mixed number is a number expressed as the sum of a whole number and a fractions, such as

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.

Rewrite the mixed number as an improper fraction.

The inverse operation of addition is subtraction. Use the subtraction property of equality to subtract from both sides.

Simplify.

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

Also, we can solve linear equations when only multiplication or division is involved. If there's a coefficient in front of the variable, multiply by the reciprocal of that number to get a coefficient of 1.

Example :

Solve.

Rewrite the mixed numbers as improper fractions.

The inverse operation of division is multiplication.

To isolate the variable x (to get a coefficient of 1), multiply both sides by which is the reciprocal of .

Multiply.

Simplify.

Therefore, the solution is .