3.1 Inequalities and Their Graphs:

Inequality: A mathematical sentence that uses and inequality symbol (< , >, ≤, ≥) to compare the values of two expressions.

Solution of an Inequality: Any number that makes the inequality true.

SYMBOLS OF INEQUALITY:( < ) Less than : Any number that is to the left not including the number itself.

x < -1

SYMBOLS OF INEQUALITY:

( > ) Greater than: Any number that is to the right not including the number itself.

x > 1

SYMBOLS OF INEQUALITY:

( ≤ ) Less than or equal to : Any number that is to the left including the number itself.

x ≤ 0

SYMBOLS OF INEQUALITY:

( ≥ ) Greater than or equal to : Any number that is to the right including the number itself.

x ≥ 2

GOAL:

WRITING INEQUALITIES: We can use the inequality symbols to write verbal expressions into math sentences and use the number line to represent the solution.

Ex:All real numbers greater than 3.

http://player.discoveryeducation.com/index.cfm?guidAssetId=A9FA7702-1F9F-4A4D-9E51-2FF98439A759

WRITING INEQUALITIES: (SOLUTION) All real numbers greater than 3.

Let x = real numbers

Greater than > x > 3

Graph:

REAL-WORLD:

Joseph saved last month a total of $115 dollars for doing house shores. He is planning to spend $30 on a video game and the he wants to buy music sheet booklets. If each booklet costs $15, create a graph to represent the number of booklets he can buy.

Solution: Joseph saved $115Buys video game - 30 Music sheet booklets $15x

To find how many he can buy: 15x + 30 ≤ 150

15x ≤ 120

x ≤ 8 booklets.

Subtract 30Divide by 15

YOU TRY IT:

Ex:What inequality represent the verbal

expression:

The subtraction of t and 7 is less than -3.

SOLUTION:The sum and t and 7 is less than -3.

t, 7, - 3subtraction -Less than <

t - 7 < -3

Graph: ( isolate t t < 4)

IDENTIFYING SOLUTIONS: We can use substitution to see if a given number is a solution to an equation.Ex: Identify solutions by evaluation:

13 – 7y ≤ 6

a) 1 b) -1, c) 3 d) -5

SOLUTION:

a) 1 13 – 7( 1) ≤ 613 – 7 ≤ 6 6 ≤ 6 TRUE

13 – 7y ≤ 6

a) -1 13 – 7( -1) ≤ 6 13 + 7 ≤ 6 20 ≤ 6 FALSE

13 – 7y ≤ 6Thus 1 is a solution.

Thus -1 is NOT a solution.

SOLUTION:

a) 3 13 – 7( 3) ≤ 613 – 21 ≤ 6

-7 ≤ 6 TRUE

13 – 7y ≤ 6

a) 5 13 – 7( 5 ) ≤ 613 - 35 ≤ 6

- 12 ≤ 6 TRUE

13 – 7y ≤ 6Thus 3 is a solution.

Thus 5 is a solution.

GRAPHING: Always isolate variables and then graph. x < -1

x > 1

x ≤ 0

x ≥ 2

VIDEOS: Graphing Inequalities

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-linear-inequalities/v/solving-and-graphing-linear-inequalities-in-two-variables-1

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-linear-inequalities/v/graphing-inequalities

CLASSWORK:

Page 167-170

Problems: As many as needed to master the

concept.