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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 1:

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 2:

Solve:

$6.3 y = 8.19$

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

$\frac{6.3 y}{6.3} = \frac{8.19}{6.3}$

Simplify.

$y = 1.3$

Example 3:

Solve:

$\frac{a}{3.5} = 2.4$

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

$(\frac{a}{3.5}) (3.5) = (2.4) (3.5)$

Simplify.

$a = 8.4$