Solving Multi-Step Linear Equations

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

To solve the equation x – 5x + 7 = 39, we need more than two operations.

By Identity Property, x = 1x .

Combine the like terms.

Undo addition. Subtract 7 from each side.

Simplify.

Undo multiplication. Divide each side by –4.

Simplify.

We have solved the equation.

Example :

Solve 2(4 m + 5) = 3 m – 20. Check the solution.

Solution

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

Subtract 3m from each side and simplify.

Undo addition. Subtract 10 from each side.

Undo multiplication. Divide each side by 5.

Simplify.

To check the solution, substitute –6 for m in the equation.

Simplify.