Solve Equations With Variables on Both

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Presentation transcript:

Solve Equations With Variables on Both Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite SOlutions bkevil

2x + 14 + 3 = 5x – 1 2x + 17 = 5x - 1 -5x -5x -3x + 17 = - 1 - 17 - 17 Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite SOlutions 2(x + 7) + 3 = 5x - 1 2x + 14 + 3 = 5x – 1 1) Get rid of ( ) --distribute 2x + 17 = 5x - 1 2) Combine like terms -5x -5x 3) Get variables on same side – use inverse operation -3x + 17 = - 1 - 17 - 17 4) Solve 2 step equation -3x = -18 Undo by using inverse  -3 undo 2nd -3 -3  -3 + 17 - 17 undo 1st x = 6 bkevil

9 + 5x = 5x + 9 -5x -5x 9 = 9 x = Infinite Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite SOlution 9 + 5x = 5x + 9 Get variables on same side of equation – use inverse operation (subtract 5x) -5x -5x 9 = 9 The variables zeroed out and remaining is a true statement where a number is equal to itself – this is called an identity x = Infinite The solution is all real numbers bkevil

6x – 1 = 6x – 8 -6x -6x -1 = - 8 x = no solutions Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite SOlutions 6x – 1 = 6x – 8 Get variables on same side of equation – use inverse operation (subtract 6x) -6x -6x -1 = - 8 The variables zeroed out and remaining is a false statement where a number is equal to a different number, so there will be no number that will work in the equation. x = no solutions The solution is no real numbers or empty set bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution bkevil

INFINITE!!! bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution bkevil

ONE SOLUTION!! bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution ONE!! bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution ONE SOLUTION bkevil

Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution bkevil

NO SOLUTION bkevil