2. HW: Page 734 1-53 ODD Answers

3. Pre-Algebra 2-5 Solving Inequalities Containing Integers Pre-Algebra: 2-5 HW Page 80 #13-30 all

4. Pre-Algebra 2-5 Solving Inequalities Containing Integers Today’s Learning Goal Assignment Learn to solve inequalities with integers.

5. Pre-Algebra 2-5 Solving Inequalities Containing Integers 2-5 Solving Inequalities Containing Integers Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

6. Pre-Algebra 2-5 Solving Inequalities Containing Integers Warm Up Compare, Use >, <, or =. Pre-Algebra 2-5 Solving Inequalities Containing Integers > > = < > 1. –3 –42. 6 –2 3. –8 –54. –5 –5 5. 3 –36. –8 –2 <

7. Pre-Algebra 2-5 Solving Inequalities Containing Integers Problem of the Day Elliot led the race; Gordon was ahead of Wallace. Labonte was directly behind Gordon and directly ahead of Marlin. Who was in last place ? Wallace

8. Pre-Algebra 2-5 Solving Inequalities Containing Integers Today’s Learning Goal Assignment Learn to solve inequalities with integers.

9. Pre-Algebra 2-5 Solving Inequalities Containing Integers When you pour salt on ice, the ice begins to melt. If enough salt is added, the resulting saltwater will have a freezing point of –21°C, which is much less than water’s freezing point of 0°C. At its freezing point, a substance begins to freeze. To stay frozen, the substance must maintain a temperature that is less than or equal to its freezing point. Adding rock salt to the ice lowers the freezing point and helps to freeze the ice cream mixture.

10. Pre-Algebra 2-5 Solving Inequalities Containing Integers If you add salt to the ice that is at a temperature of –4°C, what must the temperature change be to keep the ice from melting? This problem can be expressed as the following inequality: –4 + t  –21 When you add 4 to both sides and solve, you find that if t  –21, the ice will remain frozen.

11. Pre-Algebra 2-5 Solving Inequalities Containing Integers The graph of an inequality shows all of the numbers that satisfy the inequality. When graphing inequalities on a number line, use solid circles ( ) for  and  and open circles ( ) for > and <. Remember!

12. Pre-Algebra 2-5 Solving Inequalities Containing Integers k > –5 A. k +3 > –2 Subtract 3 from both sides. –3 k +3 > –2 Solve and graph. Additional Example 1A: Adding and Subtracting to Solve Inequalities –5 0

13. Pre-Algebra 2-5 Solving Inequalities Containing Integers B. r – 9  12 r  21 Add 9 to both sides. r – 9 + 9  12 + 9 r – 9  12 21 24 15 Additional Example 1B: Adding and Subtracting to Solve Inequalities Continued Solve and graph.

14. Pre-Algebra 2-5 Solving Inequalities Containing Integers C. u – 5  3 u  8 Add 5 to both sides. u – 5 + 5  3 + 5 u – 5  3 8 10 5 0 Solve and graph. Additional Example 1C: Adding and Subtracting to Solve Inequalities Continued

15. Pre-Algebra 2-5 Solving Inequalities Containing Integers c  –4 D. c + 6  2 Subtract 6 from both sides. –6 c + 6  2 04 –7 –4 Solve and graph. Additional Example 1D: Adding and Subtracting to Solve Inequalities Continued

16. Pre-Algebra 2-5 Solving Inequalities Containing Integers y  –8 A. y + 7  –1 Subtract 7 from both sides. –7 y + 7  –1 Try This: Example 1A 0 –11 –8 Solve and graph.

17. Pre-Algebra 2-5 Solving Inequalities Containing Integers B. f – 4  8 r  12 Add 4 to both sides. f – 4 + 4  8 + 4 f – 4  8 1215 6 Try This: Example 1B Solve and graph.

18. Pre-Algebra 2-5 Solving Inequalities Containing Integers C. r – 2 < 1 r < 3 Add 2 to both sides. r – 2 + 2 < 1 + 2 r – 2 < 1 –303 8 Try This: Example 1C Solve and graph.

19. Pre-Algebra 2-5 Solving Inequalities Containing Integers d  –3 D. d + 9  6 Subtract 9 from both sides. –9 d + 9  6 –30 –74 Try This: Example 1D Solve and graph.

20. Pre-Algebra 2-5 Solving Inequalities Containing Integers –5 1 5 is greater than –1. Sometimes you must multiply or divide to isolate the variable. Multiplying or dividing both sides of an inequality by a negative number gives a surprising result. 5 > –1 Multiply both sides by –1. –1 5 –1 (–1) > or < ? You know –5 is less than 1, so you should use <. –5 < 1 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –5 < 1 5 > –1

21. Pre-Algebra 2-5 Solving Inequalities Containing Integers 3 > 1 –4  12 Multiply by –2 Divide by –4 1  –3 –6 < –2 MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS Words Original Inequality Multiply/ Divide Result Multiplying or dividing by a negative number reverses the inequality symbol.

22. Pre-Algebra 2-5 Solving Inequalities Containing Integers The direction of the inequality changes only if the number you are using to multiply or divide by is negative. Helpful Hint

23. Pre-Algebra 2-5 Solving Inequalities Containing Integers A. –3y  15 y  –5 Divide each side by –3;  changes to . B. 7m < 21 m < 3m < 3 Divide each side by 7. Additional Example 2: Multiplying and Dividing to Solve Inequalities Solve and graph. 0 3–3 5 –3y  15 –3–3–3–3 7m < 21 7 7 –7 –5 04

24. Pre-Algebra 2-5 Solving Inequalities Containing Integers A. –8y  24 y  –3 Divide each side by –8; changes > to <. B. 9f > 45 f > 5f > 5 Divide each side by 9. Try This: Example 2 –8y  24 –8–8–8–8 9f > 45 9 9 –3 0 –74 0510 Solve and graph.

25. Pre-Algebra 2-5 Solving Inequalities Containing Integers Lesson Quiz: Part 1 Solve and graph. 1. h + 2 < 0 2. c – 5 > –2 7n > 28 t –3 3. < 1 h  –2 n > 4 t > –3 c  3 –2–2 02 3 –3–3 0 3 –3–3 0 4 8 0 4.

26. Pre-Algebra 2-5 Solving Inequalities Containing Integers A local weather forecast stated that it would be 12°F tonight and at least 10° colder the next night. Write an inequality to show how cold it will be ? Lesson Quiz: Part 2 5. x  2°F