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Algebra
3.4 Notes
Name:_______________________________________
Mitchell/Grice
3.4: Solving Equations with Variables on Both Sides
Objective:
o Solve equations with variables on both sides of the equal sign.
(1) SIMPLIFY BOTH SIDES OF THE EQUATION, IF NECESSARY.
(Distributive Property, Combine Like Terms, Standard Form)
(2) GET THE VARIABLE TO ONE SIDE OF THE EQUATION USING INVERSE OPERATIONS.
(Get the x’s to one side)
(3) USE INVERSE OPERATIONS TO ISOLATE THE VARIABLE.
(Get x by itself)
o
Solve each of the following equations for x.
1) 2x −12 = 5x
2) −3x + 35 = 2x
3) 3x − 7 = 5x + 9
4) x − 8 = 4x −14
5) 2x − 6 = −3x + 14
6) −3x − 8 = 5x − 32
7) −4x + 7 = −2x + 15
8) −5x − 4 = −6x −11
o
Solve each of the following equations for x.
1) 5x + 3 − 2x = x −17
2) −2x + 9 = 5x + 1 − 9x
3) 4x − 5 − x = 4x −12
4) 7x −1 = 3x −10 − 5x
5) 2x − 3x + 7 = 3x + 15
6) −6x + 7 = 9 − 5x −13
7) 7 − 9x − 3 = −3x −14
8) 2x − 9 = 3x + 15 − 5x
o
All of the equations that we have been solving have had one solution. It is possible for an equation
to have one solution,
solution no solutions,
solutions or many solutions.
solutions
o
NO SOLUTIONS: __________________________________________________________________________
__________________________________________________________________________
EX:
o
3x − 7 = 3x + 11
MANY SOLUTIONS: ________________________________________________________________________
________________________________________________________________________
EX:
o
2x − 5 = 2x − 5
Determine if the following equations have one solution,
solution no solutions,
solutions or many solutions
solutions.
utions
1) 2x − 3 = 5x − 7 − 3x
2) 7x + 5 − 2x = 5x + 5
3) x − 4 = 4x + 7 − 5x
4) 4x + 9 = −2x + 5 + 6x
5) 3x − 6 − 5x = −2x − 6
6) −4x + 7 = 5x −1 − x