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Linear Equations and Inequalitie
Solving Inequalities
Absolute Value Inequalities
Graphing Equivalent Fractions Lesson Plan
Investigating Liner Equations Using Graphing Calculator
Graphically solving a System of two Linear Equatio
Shifting Reflecting Sketching Graph
Graphs of Rational Functions
Systems of Equations and Inequalities
Graphing Systems of Linear Equat
LINEAR FUNCTIONS: SLOPE, GRAPHS AND MODELS
Solving Inequalities with Absolute Values
Solving Inequalities
Solving Equations & Inequalities
Graph the rational function
Inequalities and Applications
Inequalities
Using MATLAB to Solve Linear Inequalities
Equations and Inequalities
Graph Linear Inequalities in Two Variables
Solving Equations & Inequalities
Teaching Inequalities:A Hypothetical Classroom Case
Graphing Linear Inequalities and Systems of Inequalities
Inequalities and Applications
Solving Inequalities
Quadratic Inequalities
Inequalities
Solving Systems of Linear Equations by Graphing
Systems of Equations and Inequalities
Graphing Linear Inequalities
Inequalities
Solving Inequalities
Solving Inequalities
Solving Equations Algebraically and Graphically
Graphing Linear Equations
Solving Linear Equations and Inequalities Practice Problems
Graphing Linear Inequalities
Equations and Inequalities
Solving Inequalities

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Inequalities

Definitions

Rational Numbers: A number that can be expressed as the quotient of two integers
Examples of Rational Numbers: 1, 5, -4, -8,2/3,-4/3, 3.45, 2.346
Irrational Numbers: A number that can not be expressed as the quotient of two
integers,
Examples of Irrational Numbers:

Example 1 Identify each number as rational or irrational
a) - 343 ( This is a rational number)
b) (This number is irrational)
c) 24/7 (This number is rational)
d) 2e (This number is irrational)

Inequalities
Symbols

> Greater than
≥ Greater than or equal to
< Less than
≤ Less than or equal to

The number line

Solving Inequalities

Inequality Properties

Transitive Property a > b and b > c a > c

Addition Property for Inequalities a > b a + c > b + c

Multiplication properties for Inequalities

(If c is positive, then a > b ac > bc, c > 0 )
(If c is negative, then a > b ac < bc, c < 0 )

Subtraction property for Inequalities a > b a − c > b − c

Example 2

Solve the following inequality 2x + 4 >10

add to both sides
simplify
divide by 2
simplify

Example 3

Solve the following inequality 12x + 36 ≤ 6x + 48

subtract x from both sides
simplify
substract 36 from both sides

divide by 6

Example 4

Solve the following inequality

Compound Inequalities

Example 5

Solve

Example 6

Solve

Example 7

Solve the following inequality 0 ≤ x + 3 ≤ 5

Example 8

Solve the following inequality − 4 ≤ 3x + 3 ≤ 5