# Solving One–Step Linear Equations with Decimals

A linear equation is an algebraic equation in which the variable(s) are multiplied by numbers or added to numbers, with nothing more complicated than that.

A solution to an equation is a number that can be plugged in for the variable to make a true number statement.

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

Example:

Solve:

p + 4.5 = 9.3

The inverse operation of addition is subtraction. So, subtract –4.5 from both sides.

p + 4.5 – 4.5 = 9.3 – 4.5

Simplify.

p = 4.8

We can also solve linear equations when 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 1:

Solve:

The inverse operation of multiplication is division. So, divide both sides by 6.3.

Simplify.

y = 1.3

Example 2:

Solve:

To isolate the variable a (to get a coefficient of 1), multiply both sides by 3.5.

Simplify.