1. 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.

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

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

4. Comparison Practice 5.6 + 8 15 6.6 + 4 8 + 4 7.(8)(3) (6) (4) 8.16 ÷ 2 36 ÷ 4 9.17 – 3 21 – 9 10.(4)(5) 23 – 7 1.12 15 2.43 68 3.4 + 2 8 4.4 12 ÷ 4 4

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

6. ALGEBRAIC INEQUALITIES ≥ 7 s ≥ s 65 6

7. Now Write 5 more of your own Algebraic Inequalities 1. 2. 3. 4. 5. 7

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

9. Sometimes we know the answer to an inequality. The number that makes the inequality true is call the SOLUTION. 21 - 614 1514 9

10. Sometimes we know the answer to an inequality. The number that makes the inequality true is call the SOLUTION. 913 - 4 99 10

11. Find the Solution of each Inequality Circle the Solution you found. ProblemWritten with Solution Circled 1) 24 17 + 4 2) 32 – 10 28 3) (12)(3) 30 4) 13 54 ÷ 9 5) 3x – 12 = 24 √64 11

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

13. 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

14. 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

15. Here are 2 Examples of SOLUTION SET answers. InequalitySolution Set Answer x < 5 m ≥ -1 15 X could be ANY number less than five, but NOT 5 M could be ANY number greater than -1, including -1.

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 Arrows are logical. 16

17. 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

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

19. 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

20. 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