Download Pre-Algebra 3-3 Notes Completed

Solving Equations by Adding or Subtracting (3-3)
Definition: Inverse operations “undo” each other _______________ and _______________
are inverse operations, because they “undo” each other.
Subtraction Property of Equality:
 If you subtract the same number for each side of an equation, the two sides remain equal
Ex.
5=5
Ex.
x+2=3
__________= ___________
__________= ___________
_____ = _____
_____ = _____
Addition Property of Equality:
 If you add the same number for each side of an equation, the two sides remain equal
Ex.
5=5
Ex.
__________= ___________
_____ = _____
n–2=5
__________= ___________
_____ = _____
Definition: Equivalent Equations have the same solution.
 When you use the Subtractions Property or Addition Property of Equality, you make
equivalent equations.
Remember that a SOLUTION is the value of the variable that makes the equation true.
x+3=7
The solution is x = _____
To Solve Equations you use the Subtraction Property and Addition Property of Equality to
“UNDO” what had been added to or subtracted from x, to find the value of the variable
Solve each equation. Check your solution.
Ex.
x+4=7
_______________ = _____________ (Subtraction Property)
_______ = _______ (Solution)
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Ex.
16 + x = 14
__________ = _____ (Commutative Property)
_______________ = _____________ (Subtraction Property)
_______ = _______ (Solution)
Ex.
y – 7 = -25
_______________ = _____________ (Addition Property)
_______ = _______ (Solution)
Ex.
x + 8 = -5
_______________ = _____________ (Subtraction Property)
_______ = _______ (Solution)
Ex.
16 = y + 20
__________ = _____ (Transitive Property)
_______________ = _____________ (Subtraction Property)
_______ = _______ (Solution)
Ex.
y – 49 = -13
_______________ = _____________ (Addition Property)
_______ = _______ (Solution)
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