Objectives: To solve and graph simple and compound inequalities.

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Presentation transcript:

Objectives: To solve and graph simple and compound inequalities

What are Inequalities? Five symbols

Solving Inequalities Solving inequalities is exactly the same as solving equations, with one major exception. What is the major exception??? How do you graph on a number line?

Interval Notation Interval Notatation: The symbols ____, _____, and ______ mean a number is not included in the set. The symbols ____, _____, and _______ mean a number is included in the set. Examples: Write the following in interval notation: ExpressionInterval Notation x< 4 x > 4

Examples 1. 3x + 4(6 – x) < 22. 4p + 2(p + 7) < ≤ 5 – 2(4m + 7)4. 8 > 3(5 – b) + 2

No Solutions and All Real Number Solutions If the variables cancel out in an inequality… and the statement is false… there are no solutions and the statement is true… all real numbers are the solution What will these graphs look like???

Examples 2x < 2(x + 1) + 34(x – 3) + 7 ≥ 4x + 1

Compound Inequalities A pair of inequalities joined by and or or. x 9 x -1 another way to write -1 < x < 7 Pay attention! Is the answer really no solutions or all real numbers???

Examples 3n –7 > n + 1 or 4n – 5 < 3n – 3 3 < 5 + 6h  10

Homework Pgs , #1-13 odd,29-34—do not graph, 41-49