1. Chapter2 2-5 solving inequalities with variables on both sides

2. Objectives Solve inequalities that contain variable terms on both sides.

3. Inequalities Some inequalities have variable terms on both sides of the inequality symbol. You can solve these inequalities like you solved equations with variables on both sides. How to solve this inequalities? Use the properties of inequality to “ collect ” all the variable terms on one side and all the constant terms on the other side.

4. Example#1 Solve the inequality and graph the solutions y ≤ 4 y + 18

5. Example#2 Solve the inequality and graph the solutions. 4 m – 3 < 2 m + 6

6. Example#3 Solve the inequality and graph the solutions 4 x ≥ 7 x + 6

7. Example#4 Solve the inequality and graph the solutions 5 t + 1 < –2 t – 6

8. Student guided practice Do problems 1-6 from book page 129

9. Business Application The Home Cleaning Company charges $312 to power-wash the siding of a house plus $12 for each window. Power Clean charges $36 per window, and the price includes power-washing the siding. How many windows must a house have to make the total cost from The Home Cleaning Company less expensive than Power Clean?

10. Application A-Plus Advertising charges a fee of $24 plus $0.10 per flyer to print and deliver flyers. Print and More charges $0.25 per flyer. For how many flyers is the cost at A-Plus Advertising less than the cost of Print and More?

11. Inequailities You may need to simplify one or both sides of an inequality before solving it. Look for like terms to combine and places to use the Distributive Property.

12. Example#4 Solve the inequality and graph the solutions. 2( k – 3) > 6 + 3 k – 3

13. Example#5 Solve the inequality and graph the solutions 5(2 – r ) ≥ 3( r – 2)

14. Example#6 Solve the inequality and graph the solutions. 0.5 x – 0.3 + 1.9 x < 0.3 x + 6

15. Properties of inequalities Some inequalities are true no matter what value is substituted for the variable. For these inequalities, all real numbers are solutions. Some inequalities are false no matter what value is substituted for the variable. These inequalities have no solutions. If both sides of an inequality are fully simplified and the same variable term appears on both sides, then the inequality has all real numbers as solutions or it has no solutions. Look at the other terms in the inequality to decide which is the case.

16. Examples Example#7 2 x – 7 ≤ 5 + 2 x

17. Homework Lets do problems 8-19 evens only from page 129

18. Closure Today we saw how to solve inequalities with variables on both sides of the equation Next class we are going to see compound inequalities.

19. Have a great day!!