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

2. 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 = 5x – 1
1) Get rid of ( ) --distribute
2x + 17 = 5x - 1
2) Combine like terms
-5x x
3) Get variables on same side – use inverse operation
-3x + 17 = - 1
4) Solve 2 step equation
-3x = -18
Undo by using inverse
 undo 2nd
 -3
+ 17
undo 1st
x = 6
bkevil

3. 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

4. 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 x
-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

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

6. INFINITE!!!
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7. Red card- No Solution Yellow Card- 1 Solution Green Card-Infinite Solution
bkevil

8. ONE SOLUTION!!
bkevil

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

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

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

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

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

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

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

16. NO SOLUTION
bkevil