1. Inequalities September 20, 2010

2. ACT Opener Solve 2n – 6 = 10 – 14n. A. 1 B. -1 C. 0 D. -2 E. 2 Solve (2/3)h – 5 = h + 7 F. -36 G. 36 H. -24 J. 24 K. 20 Solve for x: 5x + 3 = 2x -9 Solve for k: 5k + 12 – 2k = 37 + 2k - 11

3. Inequality Symbols < less than > greater than open dot ≤ less than or equal to ≥ greater than or equal to closed dot

4. Inequality Symbols The Open Dot We only use the “open dot” to graph less than and greater than inequalities. < or > The Closed Dot We only use the “closed dot” to graph less than or equal to and greater than or equal to inequalities < or >

5. Inequality Shading If x is greater than (greater than or equal to), then shade to the right. If x is less than (less than or equal to), the shade to the left.

6. An Inequality Special Situation If you multiply or divide by a negative number, reverse the symbol. Otherwise, we solve inequalities just like equations!

7. Examples: Assume the domain is all real numbers x > 3 a < -1 -5 < b

8. Examples: Assume the domain is all real numbers 4 > x x = -4 x ≠ 3

9. Solve and Graph Examples 3x-5 < 2

10. Solve and Graph Examples 5x + 4 > 19

11. Solve and Graph Examples 2x – 7 < 3

12. Examples 4 - 3x > -2

13. Examples 6x – 3 < 7 + 4x

14. Examples 2(w-8) + 9 > 3(4 – w) - 4

15. Examples 8 – 2b > 4 - b

16. Examples 4(2 – v) > -(v – 5)

17. Exit Slip

18. Solving Inequalities with Multiple Operations AND Solving Inequalities with Variables on Both Sides Page 26 and 27 b Assignment