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 $25$ .

$\frac{25 m}{25} = \frac{200}{25}$

Simplify.

$m = 8$