Multi-Step Equations & Special Solutions

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Presentation transcript:

Multi-Step Equations & Special Solutions

Find the error in the examples below. What’s wrong with his/her work? Find the correct solution for each!

Strategies for Equations with Variables on Both Sides Simplify each side IF NEEDED! Identify your variables and constants by circling all variables and putting rectangles around constants!

Strategies Cont. Use the Addition and Subtraction Properties of Equality to get the variables on ONE side! Move the Variables to One Side! Move the Constants to the OTHER side! Then Solve!

Solve: 6x + 3 = 8x -21 Always check to see if your left or right side can be simplified! 6x + 3 = 8x -21 Variables on Both Sides!

Example: Example:

Special Solutions: NO SOLUTION Some equations have no solution that can make it true! Example: x + 5 = x + 6

Special Solutions: ALL REAL NUMBERS Some equations have lots of solutions that make it true! Example: 3x + 1 = 3x + 1 We call this type an identity and it has MANY Solutions!

Example: Example: In cases such as these, the variable ALWAYS cancels out!

Application You can buy used in-line skates from your friend for $40, or you can rent some. Either way, you must rent safety equipment. How many hours must you skate for the cost of renting and buying skates to be the same? Let h = the number of hours you must skate.