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Solving Multi-Step Linear Equations

We sometimes need more than two operations to solve alinear equation. Useinverse operationsto undo each operation in reverse order.

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

By the Identity Property, x = 1 x .

1 x 5 x + 7 = 39

Combine the like terms.

4 x + 7 = 39

Undo the addition. Subtract 7 from each side.

4 x + 7 7 = 39 7

Simplify.

4 x = 32

Undo the multiplication. Divide each side by 4 .

4 x 4 = 32 4

Simplify.

x = 8

We have solved the equation.

Example:

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

Solution

Use thedistributive lawon the left side of the equation.

2 ( 4 m ) + 2 ( 5 ) = 3 m 20 8 m + 10 = 3 m 20

Subtract 3 m from each side and simplify.

8 m 3 m + 10 = 3 m 3 m 20 5 m + 10 = 20

Undo the addition. Subtract 10 from each side.

5 m + 10 10 = 20 10 5 m = 30

Undo the multiplication. Divide each side by 5 .

5 m 5 = 30 5

Simplify.

m = 6

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

2 ( 4 ( 6 ) + 5 ) = ? 3 ( 6 ) 20

Simplify.

2 ( 24 + 5 ) = ? 18 20 2 ( 19 ) = ? 18 20 38 = ? 38