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Solving Multi-Step Linear Equations with Decimals

We need more than two operations to solve a linear equation . Use inverse operations to undo each operation in reverse order.

Steps for solving a Multi-Step Equation:

Step 1 Clear the equation of decimals.

Step 2 Use the Distributive Property to remove parentheses on each side.

Step 3 Combining like terms on each side.

Step 4 Undo addition or subtraction.

Step 5 Undo multiplication or division.

Example :

Solve 0.25 m 0.4 = 1.6 .

Solution

First, Multiply both sides of the equation by 100 .

100 ( 0.25 m 0.4 ) = 100 ( 1.6 )

Use the distributive law on the left side of the equation.

25 m 40 = 160

Undo Subtraction. Add 40 to each side.

25 m 40 + 40 = 160 + 40

Simplify.

25 m = 200

Undo multiplication. Divide each side by 25 .

25 m 25 = 200 25

Simplify.

m = 8