This document provides information and examples about solving inequalities: 1) It gives examples of solving linear equations with one variable and two variables. 2) It explains the symbols used for different inequality types and how to graph them, including shading the correct side of the inequality. 3) It provides rules for solving inequalities, such as reversing the inequality sign when multiplying or dividing both sides by a negative number. 4) Multiple examples are worked through step-by-step of solving and graphing various inequalities with one variable and multiple variables.

1. InequalitiesSeptember 20, 2010

2. ACT OpenerSolve 2n – 6 = 10 – 14n. A. 1 B. -1 C. 0 D. -2 E. 2 Solve (2/3)h – 5 = h + 7F. -36G. 36H. -24J. 24K. 20Solve for x: 5x + 3 = 2x -9Solve 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 SymbolsThe Open DotWe only use the “open dot” to graph less than and greater than inequalities.< or >The Closed DotWe only use the “closed dot” to graph less than or equal to and greater than or equal to inequalities < or >

5. Inequality ShadingIf 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 SituationIf 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 numbersx > 3a < -1-5 < b

8. Examples: Assume the domain is all real numbers4 > xx = -4x ≠ 3

9. Solve and Graph Examples3x-5 < 2

10. Solve and Graph Examples5x + 4 > 19

11. Solve and Graph Examples2x – 7 < 3

12. Examples4 - 3x > -2

13. Examples6x – 3 < 7 + 4x

14. Examples2(w-8) + 9 > 3(4 – w) - 4

15. Examples8 – 2b > 4 - b

16. Examples4(2 – v) > -(v – 5)

17. Exit Slip

18. Solving Inequalities with Multiple Operations ANDSolving Inequalities with Variables on Both SidesPage 26 and 27 bAssignment