2. Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 3.6 Solving Multi-Step Inequalities Skill Check Skill Check

3. Skill Check 2. 23 = d + 7 3. -2 w > -4 x = 1 d = 16 w < 2 1. x – 5 = -4 4. a ÷ -5 < -8 a > 40 Solve.

4. Vocabulary Is a mathematical statement formed by placing an inequality symbol between two expressions. Symbols are: <, >, <, >

5. Study Strategy Be Careful when combining steps, moving variable terms and constant terms in a single step, until you become proficient at the solution process. Check your answer, always

6. Solving a multi-step Inequality EXAMPLE 1 SOLUTION a. -6 > ( g ÷ -5) – 2 Solve. a. -6 > ( g ÷ -5) – 2 g > 20 y < 3 b. 3 y – 5 < 2(17 – 5 y )c. (-5 s – 8) ÷ 4 > -22 b. 3 y – 5 < 2(17 – 5 y ) c. (-5 s – 8) ÷ 4 > -22 s < 16 20 0 3 0 16 0 -4 > g ÷ -5 3 y – 5 < 34 – 10 y 13 y < 39 -5 s – 8 > -88 -5 s > -80

7. Writing and Solving a Multi-Step Inequality EXAMPLE 2 Weather A city’s record rainfall for the month of October is 16.8 inches. So far in October this year, 11.2 inches of rain have fallen. Find the average number of inches of rain that must fall each day to break the record if there are 14 days left in the month. r > 0.4 0.4 0 Rainfall so far in October + Days in October left to break record Amount of inches of rain each day r >Record rainfall for October 11.2 + 14( r ) > 16.8 The average number of inches of rain that must fall each day to break the record if there are 14 days left in the month is more than 0.4 inches. 14 r > 5.6

8. Combining Like Terms in a Multi-Step Inequality EXAMPLE 3 Exercise A gym charges 15000 won for membership. Members pay 8000 won for exercise classes and nonmembers pay 12000 won. How many exercise classes does Jackie need to attend for the cost of membership to be less than paying as a nonmember. n > 3.7 Membership+Membership Cost for Classes Number of Classes n < 15000 + 8000 n < 12000 n Jackie needs to attend at least 4 exercise classes for the cost of membership to be less than paying as a nonmember. 4000n > 15000 Nonmembers cost for classes Number of Classes n

9. Lesson Quiz 1. 2 + 3 k > 35 2. 12 < 9 – ( m ÷ 3) 3. Is -3 a solution of 6 + 4 z > 7 z + 11? k > 11 m < -9 Yes Solve the Inequality. Graph your solution. 4. Find all the values of x that make both of the following inequalities true: 5 < 4 x + 13 and 8 + 3 x < 20. -90 110 x = {-1, 0, 1, 2, 3, 4} or -2<x<4 -204

10. Closure 1.) What must you do with the variables when solving a multi-step inequality that has variables on both sides? You must get the variables preferably on the left side of the inequality and the constant terms on the other side.

11. Challenge 2.) For what value(s) of a do the inequalities a x – 9 > 3 and 10 < (x/ a) + 7 have the same solution? a = ±2

12. Lesson 3.6 Homework: pp.153-155 Exs. (10, 12, 18, 20, 22, 26, 28, 30, 32, 34, 48, 49)