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Transcript 
SOLVE EQUATIONS
WITH VARIABLES ON
BOTH
RED CARD- NO SOLUTION
YELLOW CARD- 1 SOLUTION
GREEN CARD-INFINITE SOLUTIONS
bkevil
RED CARD- NO SOLUTION
YELLOW CARD- 1 SOLUTION
GREEN CARD-INFINITE SOLUTIONS
2(X + 7) + 3 = 5X - 1
2x + 14 + 3 = 5x – 1
2x + 17 = 5x - 1
-5x
-5x
-3x + 17 = - 1
- 17 - 17
-3x = -18
-3
-3
x= 6
bkevil
1) Get rid of ( ) --distribute
2) Combine like terms
3) Get variables on same
side – use inverse operation
4) Solve 2 step equation
Undo by using inverse
 -3
 -3 undo 2nd
+ 17
- 17
undo 1st
RED CARD- NO SOLUTION
YELLOW CARD- 1 SOLUTION
GREEN CARD-INFINITE SOLUTION
9 + 5x = 5x + 9
-5x -5x
Get variables on same side
of equation – use inverse
operation (subtract 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
RED CARD- NO SOLUTION
YELLOW CARD- 1 SOLUTION
GREEN CARD-INFINITE SOLUTIONS
6x – 1 = 6x – 8
-6x
-6x
-1 = - 8
x = no solutions
The solution is no real
numbers or empty set
bkevil
Get variables on same side
of equation – use inverse
operation (subtract 6x)
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.
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
NO 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
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