1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 5–1) CCSS Then/Now New Vocabulary Key Concept: Multiplication Property of Inequalities Example 1:Real-World Example: Write and Solve an Inequality Example 2:Solve by Multiplying Key Concept: Division Property of Inequalities Example 3:Divide to Solve an Inequality

3. Over Lesson 5–1 5-Minute Check 1 Solve y – 3 > 5. Then graph the solution on a number line. A.{y | y > 2} B.{y | y > –2} C.{y | y < 8} D.{y | y > 8}

4. Over Lesson 5–1 5-Minute Check 2 Solve t + 9 ≤ 6. Then graph the solution on a number line. A.{t | t ≤ –3} B.{t | t ≥ –3} C.{t | t ≤ 3} D.{t | t ≥ 3}

5. Over Lesson 5–1 5-Minute Check 3 Solve 4n > 3n + 9. Then graph the solution on a number line. A.{n | n > 9} B.{n | n < 9} C.{n | n ≥ 9} D.{n | n ≤ 9}

6. Over Lesson 5–1 5-Minute Check 4 A.n + 7 ≤ –5; {n | n ≤ –12} B.n + 7 ≤ –5; {n | n ≤ 2} C.n + 7 ≥ –5; {n | n ≥ –12} D.n + 7 ≥ –5; {n | n ≥ 2} Write and solve an inequality for the problem. The sum of a number and 7 is at least –5.

7. Over Lesson 5–1 5-Minute Check 5 A.20 6} B.20 14} C.20 < 2n + 8; {n | n < 6} D.20 < 2n + 8; {n | n < 14} Write and solve an inequality for the problem. Twenty is less than the sum of twice a number and 8.

8. Over Lesson 5–1 5-Minute Check 6 A.m > –23 B.m > 23 C.m < –9 D.m < 9 Solve –7 < m – (–16).

9. CCSS Content Standards A.CED.1 Create equations and inequalities in one variable and use them to solve problems. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Mathematical Practices 1 Make sense of problems and persevere in solving them. 6 Attend to precision. Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

10. Then/Now You solved equations by using multiplication and division. Solve linear inequalities by using multiplication. Solve linear inequalities by using division.

11. Concept

12. Example 1 Write and Solve and Inequality HIKING Mateo is walking at a rate of mile per hour. He knows that it is at least 9 miles to Onyx Lake. How long will it take Mateo to get there? Write and solve an inequality to find the length of time. UnderstandYou know the rate that Mateo is walking and the approximate distance to the lake. PlanThe formula for distance is d = rt. Write an inequality that represents this situation.

13. Example 1 Write and Solve and Inequality t ≥ 9Original inequality Multiply each side by. t≥ 12Simplify. Solve

14. Example 1 Write and Solve and Inequality Answer:It will take Mateo at least 12 hours. CheckTo check this answer, substitute a number greater than 12 into the original inequality. If n = 16, then (16) or 12 ≥ 9, so the solution checks.

15. Example 1 A.j ≤ 300 B.j ≥ 300 C.j ≥ 200 D.j ≤ 200 SCHOOL At Midpark High School, of the junior class attended the dance. There were at least 200 juniors at the dance. How many students are in the junior class?

16. Example 2 Solve by Multiplying Answer: The solution set is {d | d ≤ –10}. change ≥ to ≤.

17. Of the students surveyed at Madison High School, fewer than eighty-four said they have never purchased an item online. This is about one-eighth of those surveyed. How many students were surveyed? 1/8n < 84 (8)(1/8n) < 84(8) n < 672

18. Mount Kinabalue in Malaysia has the greatest concentration of wild orchids on Earth. It contains more than 750 species, or about one fourth of all orchid species in Malaysia. How many orchid species are there in Malaysia? 1/4n > 750 (4)(1/4n) > 750(4) n > 3000

19. Concept

20. Example 3 Divide to Solve an Inequality Original inequality Answer: The solution set is {k | k ≥ 5}. Divide each side by 12 and do not change the direction of the inequality sign. Simplify.

21. 2/15 60t > 8 60 60 t > 2/15 {t │t > 2/15} -42 > 6r 6 6 -7 > r {r │ r < -7}

22. Solve and graph 1/5m ≥ -3 (5)(1/5m) ≥ -3(5) m ≥ -15 {m │m ≥ -15} 3/8t < 5 (8/3)(3/8t) < 5(8/3) t < 13 1/3 {t │t < 13 1/3}

23. Example 3 A.{p | p < 4} B.{p | p < 45} C.{p | p < 75} D.{p | p > 4} A. Solve 15p < 60.

24. ber Solve an inequality the same as an equation with the = Remember if you multiply or divide by a negative, flip the inequality sign

25. Example 3 Divide to Solve an Inequality B. Solve –8q < 136. Answer: The solution set is {q | q > –17}. Original inequality Divide each side by –8 and change. Simplify.

26. Example 3 A.{z | z < 16} B.{z | z < –16} C.{z | z > –16} D.{z | z > 16} B. Solve –4z > 64.

27. Solve and graph -12h > 15 -12 -12 h < -5/4

28. -3/7r < 21 (-7/3)(-3/7r) < 21(-7/3) r > -49 {r │r > -49} -n/6 ≤ 8 -1/6n ≤ 8 (-6)(-1/6n) ≤ 8(-6) n ≥ -48 {n │n ≥ -48}

29. Example 2 A. B. C.x < –30 D.x > –30

30. Solve and graph each inequality 1)½ a < 20 { a│a < 40} 2) -10 ≤ x/-2 {x│ x ≤ 20} 3) -2 ≥ -d/34 {d│d ≥ 68} 4) 32 > -2y { y │y > -16}

31. 1)How many bracelets can Caitlin buy for herself and her friends if she wants to spend no more than $22, if each bracelet cost $4.75? 4.75n ≤ 22 n ≤ 4.63 She can buy no more than 4.

32. 2) The American history classes are planning a trip to a local museum. Admission is $8 per person. Determine how many people can go for $260. 8n ≤ 260 n ≤ 32 No more than 32 people

33. End of the Lesson