1. Linear Models and Inequalities F-LE.2, F-LE.5, A-CED.2, A-CED.3, F-BF.1

2. Table of Contents 57: How Do I Solve Inequalities? 56: Guided Practice

3. EQ: How Do I Solve Inequalities? 8/8/2015

4. Example 1: Graph the two equations and answer the questions f(x) = 2x – 2 g(x) = 1 – 4x

5. When does f(x) = g(x)? f(x) = g(x) 2x – 2 = 1 – 4x + 2 _____________ 2x = 3 – 4x + 4x _____________ 6x = 3__ 6 x = 1 2

6. When does f(x) > g(x)? f(x) > g(x) 2x – 2 > 1 – 4x + 2 _____________ 2x > 3 – 4x + 4x _____________ 6x > 3__ 6 x > 1 2

7. Questions What is similar about the way you solve inequalities and equations? What do you think might be different about the way you solve inequalities and equations?

8. When does f(x) ≤ g(x)? f(x) ≤ g(x) 2x – 2 ≤ 1 – 4x - 2x _____________ -2 ≤ 1 – 6x _____________ -3 ≤ -6x__ -6 1 ≤ x 2 1 ≥ x 2

9. When are inequalities not solved like equations? When you multiply or divide by a negative number. If you multiply or divide by a negative number, you MUST change the direction of the inequality.

10. Guided Practice 1 Solve for m. Then, write your answer in set notation and graph it on a number line. 2m – 3 < 9 + 3 ____________ 2m < 12 __ 2 m < 6 {m : m < 6} 4 5 6 7 8 9

11. Guided Practice 2 Solve for g. Then, write your answer in set notation and graph it on a number line. 2g – 3 < 9 – 8g 2g < 12 – 8g 10g < 12 g < 12 10 {g : g < 6/5} 0 1 2 3 4 5

12. Guided Practice 3 Solve for x. Then, write your answer in set notation and graph it on a number line. 3x – 5 < 15 + 8x 3x < 20 + 8x -5x < 20 x > -4 {x : x > -4} -6 -5 -4 -3 -2 -1

13. Questions When do solving inequalities and solving equations differ from each other? When you are solving inequalities (and equations) does the variable have to be the first thing you move to the other side? How do you know when to use an open circle or a closed circle?

14. Classwork Do pages 33 – 35 for classwork. Whatever you do not finish is homework. Check your answers shortly on the white board

15. Classwork Answers 1. {x : x > 3} 2. {x : x > -2} 3. {x : x ≥ 6} 4. {x : x ≤ -3} 5. {x : x > 2}