Intro to Inequalities Materials Needed 1.Individual Interactive Notebooks 2.Pencil 3.Answer Sheet 1 PS 4: Solve one- and two-step linear inequalities and graph the solutions on the number line. LT 1: Graph solutions of inequalities on the number line.

Definition: Inequality in·e·qual·i·ty Noun: The relationship between two mathematical expressions that are not equal. 2

An INEQUALITY compares using these symbols: What are their labels? 3

Comparison Practice (8)(3) (6) (4) 8.16 ÷ 2 36 ÷ – 3 21 – 9 10.(4)(5) 23 – ÷ 4 4

Definition: Algebraic Inequality al·ge·bra·ic in·e·qual·i·ty Noun: An inequality that contains a variable 5

ALGEBRAIC INEQUALITIES ≥ 7 s ≥ s 65 6

Now Write 5 more of your own Algebraic Inequalities

Definition: Solution so·lu·tion Noun: 1) A means of solving a problem. 2) The correct answer to a puzzle. 8

Sometimes we know the answer to an inequality. The number that makes the inequality true is call the SOLUTION

Sometimes we know the answer to an inequality. The number that makes the inequality true is call the SOLUTION

Find the Solution of each Inequality Circle the Solution you found. ProblemWritten with Solution Circled 1) ) 32 – ) (12)(3) 30 4) ÷ 9 5) 3x – 12 = 24 √64 11

Definition: Solutions Set so·lu·tion set Noun: The set of values that make a mathematical statement true. 12

A SOLUTIONS SET is a group of possible answers. We will never know for sure what the answer will be, so we give a range of possible answers It’s like saying: I’m not sure what the solution is exactly, but it’s greater/less than __________. 13

Use the completed squares to help you fill in the blank ones. InequalityIn WordsWhat are 3 possible solutions? Why? 1) x < 5 32, -7, 3 they are all less than 5 2) a > 0 ‘a’ is greater than 0 3) y ≤ 13 4) m ≥ 3 ‘m’ is greater than or equal to 3 3, 99, 1235 they are all greater than or equal to 3 14

Here are 2 Examples of SOLUTION SET answers. InequalitySolution Set Answer x < 5 m ≥ X could be ANY number less than five, but NOT 5 M could be ANY number greater than -1, including -1.

What do you write for an answer when trying to show a SOLUTION SET? InequalitySolution Set 1) x < 5 2) a > 0 3) y ≤ 13 4) m ≥ 3 Arrows are logical. 16

What do you write for an answer when trying to show a SOLUTION SET? InequalitySolution Set 1) x < 5 2) a > 0 3) y ≤ 13 4) m ≥ 3 17

Why are points open & closed? InequalitySolution Set 1) x ≤ 16 2) a > 3 3) y ≥ 0 4) m < 22 5) k ≤ 2 18

What do you write for an answer when trying to show a SOLUTION SET? InequalitySolution Set 1) x > 4 2) a ≤ 2 3) y ≤ 3 4) m > -1 5) b ≥ 0 6) b < 0 19

Solution Sets Practice InequalitySolution Set x ≤ 3 h > -2 w < -1 p ≥ -4 m ≥ -5 y < 12 a ≤ -7 t > 21 Graph the solution set for each inequality. 1)Which direction does the arrow go? 2)Is the point open or closed? 20