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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 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.



x 3 1 2 = 17 2

Rewrite the mixed number as an improper fraction.

x 7 2 = 17 2

The inverse operation of subtraction is addition. Use the addition property of equality to add 7 2 to both sides.

x 7 2 + 7 2 = 17 2 + 7 2


x = 24 2

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

x = 12