Ways to represent Inequalities:

• All real numbers
• As an Inequality:  -∞ < x > ∞
• As a number line
• As interval notation  (-∞,∞)

*Always use open Interval type ( ) with infinities

Intereval Types

( )  Open

[ ]  Closed

What is -a?

It's the opposite of a

Ex:

      a= 4

     -a= -4

a=-4

-a= 4

(-) infront veriable changes value

Real Numbers:

Numbers that we count with starting from 1.

Example: 1,2,3,4,5.....

All counting numbers starting with 0.

Ex: 0,1,2,3,4,5.....

Rational Numbers:  a real number (1,2,3...) is written as the ratio of two intergers ( Negatives, 0, positive #'s), where the dominator doesn't can't equl to 0.

Ex: Repeats 173/55=3.145.... or terminates 1/2=0.5

Irrational: a real number the canot be writte as the ratio of two integers. They have infinite nonrepeating decimal representations

Ex: ∏= 3.1415926=3.14

<= Less than

>= Greater than

≤= Less than or equal to

≥= Greater than or equal to

a + b = b + a

Ex:

4x + x^2 = x^2 +4x

Inequality    Interval Type

a≤x≤b            Closed [ ]

a<x<b            Open   ( )

a≤x>b            Closed and Open  [ )

Variables- collection of letters

Constants- are real numbers

ab = ba

ex:

(4-x)x^2 = x^2(4-x)

are terms that have constants followed by a variable

Ex: x^2-5x+8

Variable Terms are : x^2 and -5x

(a + b) +c = a+ (b + c)

Moving the butt cheeks from one set of term to another set of term

ex:

(x + 5) + x^2 = x + (5 + x^2)

is the real number in an algebraic expression that doesn't have a variable

Ex: x^2-5x+8

Constant Term: 8

the numerical factor of a variable term

Ex:x^2-5x+8

Coefficient: of x^2 is 1

-5x is -5

(ab)c = a(bc)

Moving the butt cheeks again

Ex: (2x * 3y)(8) =(2x)(3y*8)

Distributive Properties

a(b+c) = ab + ac

or

(a+b)c = ac + bc

a + 0 = a

Ex:

5y^2+0 = 5y^2

a * 1= a

a* 1/a= 1

a can't equal to 0

Ex:

(x^2+4)(1/x^2+4)=1

Domains cancel out

a + (-a) = 0

or

5x^3+(-5x^3) = 0

(-1)a= -a

-(-a)= a

(-a)b = -(ab) = a(-b)

(-a)(-b)=ab

-(a+b)=(-a) + (-b)

Properties of Zero

zero-factor property

a + 0 = a and a - 0 = a

a *0 =0

0/a=0

a/0= undefined

if ab=0, then a= 0 or b=0

Multi: a/b * c/d =ac/bd

Divi: a/b / c/d=a/b * d/c = ad/bc

Properties of Exponents

Multiplication

Properties of Exponents

Division

Properties of Exponents

a^-n=

is one of its two eqauls

ex:

4*4*4*4= 64

3*3*3*3=27

5*5*5*5= 625

Base of

a^n

The exponent of

a^n

Highest power x: 3

Ex: 2x^3-5x^2+1

Coefficient of the term with highest power of x

Ex:

2x^3-5x^2+1

it's 2

u^2+2uv+v^2= (u+v)^2

u^2-2uv+v^2=(u-v)^2

x^3+6x^2-6x-36

(x+6)(x^2-6)

F-First Term

O-Outer Terms

I- Inner Terms

L-Last Terms

u^3+v^3=(u + v)(u^2-uv+v^2)

u^3-V^3=(u-v)(u^2+uv+v^2)