SOLVE EQUATIONS WITH VARIABLES ON BOTH

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bkevil

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2(X + 7) + 3 = 5X - 1

2x + 14 + 3 = 5x – 1

bkevil

1) Get rid of ( ) --distribute

2) Combine like terms 2x + 17 = 5x - 1 -5x -5x 3) Get variables on same

side – use inverse operation-3x + 17 = - 14) Solve 2 step equation

-3

+ 17

Undo by using inverse -3 undo 2nd - 17 undo 1st

- 17 - 17 -3x = -18 -3 -3

x = 6

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9 + 5x = 5x + 9

bkevil

-5x -5x

Get variables on same side of equation – use inverse operation (subtract 5x)

The variables zeroed out and remaining is a true statement where a number is equal to itself – this is called an identity

9 = 9

x = Infinite

The solution is all real numbers

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6x – 1 = 6x – 8

bkevil

-6x -6x

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.

-1 = - 8

x = no solutions

The solution is no real numbers or empty set

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INFINITE!!!

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ONE SOLUTION!!

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NO SOLUTION!!!

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ONE!!

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ONE SOLUTION

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NO SOLUTION