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# Inequalities

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### Inequalities

1. 1. Inequalities<br />September 20, 2010<br />
2. 2. ACT Opener<br />Solve 2n – 6 = 10 – 14n.<br /> A. 1<br /> B. -1<br /> C. 0 <br /> D. -2<br /> E. 2 <br />Solve (2/3)h – 5 = h + 7<br />F. -36<br />G. 36<br />H. -24<br />J. 24<br />K. 20<br />Solve for x: 5x + 3 = 2x -9<br />Solve for k: 5k + 12 – 2k = 37 + 2k - 11<br />
3. 3. Inequality Symbols<br />< less than<br />> greater than<br /> open dot<br />≤ less than or equal to<br />≥ greater than or equal to<br /> closed dot<br />
4. 4. Inequality Symbols<br />The Open Dot<br />We only use the “open dot” to graph less than and greater than inequalities.<br />< or ><br />The Closed Dot<br />We only use the “closed dot” to graph less than or equal to and greater than or equal to inequalities <br />< or ><br />
5. 5. Inequality Shading<br />If x is greater than (greater than or equal to), then shade to the right. <br />If x is less than (less than or equal to), the shade to the left. <br />
6. 6. An Inequality Special Situation<br />If you multiply or divide by a negative number, reverse the symbol. <br />Otherwise, we solve inequalities just like equations! <br />
7. 7. Examples: Assume the domain is all real numbers<br />x > 3<br />a < -1<br />-5 < b<br />
8. 8. Examples: Assume the domain is all real numbers<br />4 > x<br />x = -4<br />x ≠ 3<br />
9. 9. Solve and Graph Examples<br />3x-5 < 2<br />
10. 10. Solve and Graph Examples<br />5x + 4 > 19<br />
11. 11. Solve and Graph Examples<br />2x – 7 < 3<br />
12. 12. Examples<br />4 - 3x > -2<br />
13. 13. Examples<br />6x – 3 < 7 + 4x<br />
14. 14. Examples<br />2(w-8) + 9 > 3(4 – w) - 4<br />
15. 15. Examples<br />8 – 2b > 4 - b<br />
16. 16. Examples<br />4(2 – v) > -(v – 5) <br />
17. 17. Exit Slip<br />
18. 18. Solving Inequalities with Multiple Operations AND<br />Solving Inequalities with Variables on Both Sides<br />Page 26 and 27 b<br />Assignment<br />