This document discusses inequalities and provides examples of solving various inequality expressions. It begins by giving an example of a negative number that is not closed under multiplication. It then defines common inequality symbols like less than, greater than, less than or equal to, and greater than or equal to. The document proceeds to give examples of solving linear inequalities assuming the domain is all real numbers, including compound inequalities involving absolute value expressions. It concludes with examples for an exit slip problem set involving solving several inequalities.

1. InequalitiesAugust 19 and 23, 2010

2. OpenerGive an example: {Negative numbers} is NOT closed under multiplication.Solve: x2= 324State the domain and range of the function :

3. Section 1.6 - Inequalities< less than> greater than open dot≤ less than or equal to≥ greater than or equal toclosed dot

4. Examples: Assume the domain is all real numbers4x-7 > 1

5. Examples3x-5 < 2

6. Examplesx-4 > -1 or x-4 ≤ -6

7. Examples4-3x > -2

8. Examples3 ≤ x+4 < 5

9. Examples|x| > 3

10. Examples|x-1| < 4

11. Examples|3x+7|≥ 7

12. Exit Slip5 – 3x ≥ -44 – 3x < -2|5x – 3| > 22|x + 3| > -6