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Solve Equations With Variables on Both

Learn how to solve equations with variables on both sides by applying mathematical operations. Understand scenarios with no solution, one solution, and infinite solutions. Master techniques to simplify equations and find the correct answers.

kelsie-bridges
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Solve Equations With Variables on Both

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

  2. 1) Get rid of ( ) --distribute 4) Solve 2 step equation 3) Get variables on same side – use inverse operation 2) Combine like terms Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite SOlutions2(x + 7) + 3 = 5x - 1 2x + 14 + 3 = 5x – 1 2x + 17 = 5x - 1 -5x -5x -3x + 17 = - 1 - 17 - 17 -3x = -18 Undo by using inverse -3 undo 2nd -3 -3  -3 + 17 -17 undo 1st x = 6

  3. The solution is all real numbers Red card- No SolutionYellow Card- 1 SolutionGreen 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

  4. The solution is no real numbers or empty set Red card- No SolutionYellow Card- 1 SolutionGreen 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

  5. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution

  6. INFINITE!!!

  7. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution

  8. ONE SOLUTION!!

  9. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution

  10. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution NO SOLUTION!!!

  11. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution

  12. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution ONE!!

  13. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution

  14. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution ONE SOLUTION

  15. Red card- No SolutionYellow Card- 1 SolutionGreen Card-Infinite Solution

  16. NO SOLUTION

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