Transcript 2.4 Properities of Equality Notes

Section 2-4
Reasoning with
Properties from
Algebra
Properties of
Equality
Addition property
•Adding something to each
side of an equation
Example:
2 x  18  2 Given
+ 18 +
2 x  20
Therefore,
the
18
Addition
Property of (=)
was applied.
subtraction property
•Subtracting from each side
of an equation
Example:
5 x  18  3x  2 Given
 3x
 3x
2 x  18  2
Therefore, the
Subtraction
Property of (=)
was applied.
Multiplication property
•Multiplying something to
each side of an equation
s
7 Given
7

5
Example: 7
Therefore, the
Multiplication
Property
of
(=)
s  35was applied.
division property
•Dividing something on each
side of an equation
2 x  40 Given
2
Example:
2
x  20
Therefore, the
Division
Property of (=)
was applied.
Reflexive property
• Same exact thing on each
side of the equal sign!
Examples:
44
AB  AB
23  23
Symmetric property
• The sides of an equation are
switched. (Nothing else is done
with the equation.)
Examples:
23 5
5  23
AB  CD
CD  AB
Transitive property
ab
bc
ac
* Relates
to the
Law of
Syllogism!
Examples:
23 5
5  5 1
2  3  5 1
AB  CD
CD  EF
AB  EF
substitution property
• Plugging in something in
place of another thing in any
equation or expression.
Example:
x  16,
2 x  4 
216  4 
Distributive property
• a(b+c) = ab +ac *Helps to get rid of
parentheses
Example:
4(x+y)
Given
= 4•x + 4•y Therefore, the
= 4x + 4y Distribution
Property was
applied.
Simplification
• To combine like terms
Example:
x= 3 + 5
=8
Given
Therefore, the
Simplification
was applied.