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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:


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


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:


6.3 y = 8.19

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

6.3 y 6.3 = 8.19 6.3


y = 1.3

Example 3:


a 3.5 = 2.4

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

( a 3.5 ) ( 3.5 ) = ( 2.4 ) ( 3.5 )


a = 8.4

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