1. Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5– Solving Inequalities with Variables on Both Sides Solve inequalities like equations. Be wary of closed verses open circles when graphing. Must reverse the inequality sign if multiplying or dividing by a negative number!

2. When solving for variables in inequalities, treat the inequality as though it were an equation and use inverse operations to solve for the variable (like before with equations!). Solve: 3x + 4 > 13 Two (or more) Step Inequalities - Review - 4 -4 3x > 9 x > 3

3. Now solve: 2x < -10 + 3x Remember to flip the sign IF you multiply or divide by a negative number. Variables on BOTH Sides - 3x -3x -x < -10 x > 10

4. Examples Solve x < 3x + 8. Graph the solution. - 3x -3x -2x < 8 x > -4 -8 -7 -6 -5 -4 -3 -2 -1 0

5. Examples Solve -3x + 1 < 3x + 21. Graph the solution. + 3x +3x 1 ≤ 6x + 21 - 21 - 21 -20 ≤ 6x 6 6 -6 -5 -4 -3 -2 -1 0 1 2

6. My Turn – Special Answers Solve 2(x + 3) < 5 + 2x. Graph the solution. -6 -5 -4 -3 -2 -1 0 1 2 2x + 6 ≤ 5 + 2x - 2x - 2x 6 ≤ 5 Not a true statement NO SOLUTION!!!!

7. My Turn – Special Answers Solve x + 5 > x + 3. Graph the solution. -x -x 5 ≥ 3 True Statement! INFINITE SOLUTIONS

8. The Daily Info charges a fee of $650 plus $80 per week to run an ad. The People’s Paper charges $145 per week. For how many weeks will the total cost at Daily Info be less expensive than the cost at People’s Paper? x = # of weeks Daily Info People’s Paper < -80x 650 < 65x 65 10 < x x > 10 So, after 10 weeks the Daily Info will be LESS Expensive

9. Example – Linear Inequality - Guided You see an advertisement for instructions on how to tie flies for fishing. The instruction book costs $15.00. The cost of materials for each fly is 15 cents. You plan to sell each fly for 58 cents, and you want to make a profit of at least 200 dollars. How many flies will you need to tie and sell? Question – What is profit? Question – What are we trying to solve for in this problem? Question – What other key information do we know?

10. Examples Solve -x + 1 < 3x + 21. Graph the solution.

11. Your Turn Solve 4x + 1 > 7x + 6. Graph the solution.

12. Your Turn Solve 5t + 1 < -2t - 6. Graph the solution.

13. Examples Solve 6(1 - x) < 3x. Graph the solution.

14. Your Turn Solve 1.6x < -0.2x + 0.9. Graph the solution.

15. Your Turn Solve 1.6x < -0.2x + 0.9. Graph the solution.

16. Your Turn Solve 2(x – 2) < -2(1 – x). Graph the solution.

17. Quick Review Solve inequalities just as you would equations using inverse operations. When multiplying or dividing by a negative number, always remember to flip the sign around.

18. Homework P199, 28-48 even, 52-55, 61-64