Section 2-4

Reasoning with Properties from

Algebra

Properties of Equality

Addition property

202

2182

x

x

•Adding something to each side of an equation

Given+ 18 + 18 Therefore, the

Addition Property of (=) was applied.

Example:

subtraction property

2182

23185

x

xxx3

•Subtracting from each side of an equation

Givenx3 Therefore, the

Subtraction Property of (=) was applied.

Example:

Multiplication property

35

57

s

s

•Multiplying something to each side of an equation

Example:Given7 7

Therefore, the Multiplication Property of (=) was applied.

division property•Dividing something on each side of an equation

Example:

20

402

x

x Given

2 2Therefore, the Division Property of (=) was applied.

Reflexive property• Same exact thing on each

side of the equal sign!

ABAB Examples:

44 3232

Symmetric property• The sides of an equation are

switched. (Nothing else is done with the equation.)

325

532

ABCD

CDAB

Examples:

Transitive property

ca

cb

ba

* Relates

to the Law of

Syllogism!

Examples:

1532

155

532

EFAB

EFCD

CDAB

substitution property

• Plugging in something in place of another thing in any equation or expression.

Example: 4162

42

,16

x

x

Distributive property• a(b+c) = ab +ac *Helps to get rid of

parentheses

Example: 4(x+y) Given

= 4•x + 4•y

= 4x + 4y Therefore, the Distribution Property was applied.

Simplification• To combine like terms

Example: x= 3 + 5 Given

= 8

Therefore, the Simplification was applied.