2. Warm Up in your SPIRAL! Jan. 6, 2015!! START NOW

3. A few announcements for your agenda!! HW Packets- turn your completed packet in today and get a FREE HW pass or Quiz points coupon! HW Packets- turn your completed packet in today and get a FREE HW pass or Quiz points coupon! HW tonight: Finish page 146 of your MSG and BRING A NEW MSG if you have not already!! HW tonight: Finish page 146 of your MSG and BRING A NEW MSG if you have not already!! BRING PENCILS everyday!! BRING PENCILS everyday!!

4. Writing & Graphing Inequalities Learning Target: Today I am learning how to write and graph inequalities on the number line because I want to be able to represent situations that have more than one correct answer.

5. Where might I see inequalities in real life?

9. If it’s any smaller, you’ve got to throw him back! If it’s any smaller, you’ve got to throw him back!

10. Activator 1. You are going to Six Flags as soon as school is out (yaay!). You have to be at least 4 ft. tall to ride some of your favorite rides, but it isn’t only 4-foot tall people who can ride the rides! How tall can you be and ride the rides? 2. See if you can figure out how to represent this with an inequality sign and a variable. (Hint: if it were an equation it would look like this: x = 4 ft. Use one of the inequality symbols posted on the board to make it an inequality.) 3. What are the possible solutions for x (the variable)? 4 ft. tall and taller x > 4 ft. 4’, 4’1”, 4’2”... 6’, 6’1”, etc.! And everything in between!

11. What are some other situations that have more than one answer or qualifying response? What are some other situations that have more than one answer or qualifying response? Examples: Scores that qualify for an A: > 90 Money you need to get into Six Flags: > $39 Age required to get the kids’ meal: < 10 years old) Number of days to complete your project < 5 days

12. An inequality states that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols: SymbolMeaningWord Phrases < > ≤ ≥ is less than is greater than is greater than or equal to is less than or equal to Fewer than, below More than, above At most, no more than At least, no less than Course 2 12-4 Write on Page 144 of your MSG!

13. Page 144 of MSG! And: ≠ SymbolMeaningWord Phrases is not equal toIs not equal to

14. Page 145 MSG #1-8 Circle the correct answer!

15. Write an inequality for each situation. A. There are at least 15 people in the waiting room. number of people ≥ 15 or x ≥ 15 B. The tram attendant will allow no more than 60 people on the tram. number of people ≤ 60 or x ≤ 60 “At least” means greater than or equal to. “No more than” means less than or equal to. Page 144 of MSG

16. Write an inequality for each situation. Check It Out: Example 1 C. There are at most 10 gallons of gas in the tank. gallons of gas ≤ 10 or x ≤ 10 D. There are at least 10 yards of fabric left. yards of fabric ≥ 10 or x ≥ 10 “At most” means less than or equal to. “At least” means greater than or equal to. Course 2 12-4 Inequalities

17. This open circle shows that 5 is not a solution. a > 5 If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle. This closed circle shows that 3 is a solution. b ≤ 3 Course 2 12-4 Graphing Inequalities

18. Symbols Review – Page 144 or 147 of your MSG! Open Circle The number is not included in the solution. The number is not included in the solution. Closed Circle The number is included in the solution. The number is included in the solution.

19. On your own paper, graph each inequality. Additional Example 2: Graphing Simple Inequalities –2 –1 0 1 2 3 A. n < 3 3 is not a solution, so draw an open circle at 3. Shade the line to the left of 3. B. a ≥ –4 –6 –4 –2 0 2 4 6 –4 is a solution, so draw a closed circle at –4. Shade the line to the right of –4. Course 2 12-4 Inequalities

20. On your own paper, graph each inequality. Check It Out: Example 2 –3 –2 –1 0 1 2 3 A. p ≤ 2 2 is a solution, so draw a closed circle at 2. Shade the line to the left of 2. B. e > –2 –3 –2 –1 0 1 2 3 –2 is not a solution, so draw an open circle at –2. Shade the line to the right of –2. Course 2 12-4 Inequalities

21. Page 146 MSG #1-7 Write an inequality and graph on the number line!

22. Closing! HW: Finish Page 146 in MSG Bring a NEW MSG How is an inequality different than an equation? How are they the same? How is an inequality different than an equation? How are they the same?