3.3 Solving Inequalities Using: × and ÷

1. Inequality: A mathematical sentence that uses and inequality symbol (< , >, ≤, ≥) to compare the values of two expressions. 3.3 Solving Inequalities Using: × and ÷ Solution of an Inequality: Any number that makes the inequality true.

2. GOAL:

3. MULTIPLICATION: ( x ) Let a, b, and c be real numbers and c > 0 (positive). If a > b, Then ac > bc Ex: if 2 > -1 then 2(3) > -1(3)  6 > -3 If a < b, Then ac < bc Ex: if -4 < -2 then -4(3) < -1(3)  -12 < -3

4. MULTIPLICATION: We can use these properties to solve for variables. Ex: What are the solutions to:

5. SOLUTION: To find the solution we must isolate the variable: given (8)(8) inverse of division c  c > 2

6. YOU TRY IT: Ex: What are the solutions to:

7. SOLUTION: To find the solution we must isolate the variable: given (3)(3) inverse of division c

8. MULTIPLICATION: ( x ) Let a, b, and c be real numbers andc< 0 (negative). If a > b, Then ac < bc sign switches Ex: if 2 > -1 then 2(-3) < -1(-3)  -6 < 3 If a < b, Then ac > bc sign switches Ex: if -4 < -2 then -4(-3) > -1(-3)  12 > 3

9. MULTIPLICATION: Once again, we can use these properties to solve for variables. Ex: What are the solutions to: http://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-divisionhttp://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-division

10. SOLUTION: To find the solution we must isolate the variable: given (-2)(-2) inverse of division n  sign switches

11. YOU TRY IT: Ex: What are the solutions to:

12. SOLUTION: To find the solution we must isolate the variable: given (-2)(-2) inverse of division V  sign switches

13. DIVISION: ( ÷ ) Let a, b, and c be real numbers and c > 0 (positive). If a > b, Then > Ex: if 4 > 2 then >  2 > 1 If a < b, Then < Ex: if -4 < -2 then <  -2 < -1

14. YOU TRY IT: Ex: What are the solutions to:

15. SOLUTION: To find the solution we must isolate the variable: given inverse of multiplication x

16. DIVISION: ( ÷ ) Let a, b, and c be real numbers andc> 0 (negative). If a > b, Then <sign switches Ex: if 4 > 2 then >  -2 < -1 If a < b, Then > sign switches Ex: if -4 < -2 then <  2 > 1

17. YOU TRY IT: Ex: What are the solutions to:

18. SOLUTION: To find the solution we must isolate the variable: given inverse of multiplication x sign switches

19. Real-World: You walk dogs in your neighborhood after school. You earn $4.50 per dog. How many dogs do you have to walk to earn at least $115?

20. SOLUTION: Data: $4.40 per dogx = number of dogs At least  more than $4.50x > $115 Inverse of multiplication. > X > 25.5 dogs  walk at least 26 dogs.

21. REMEMBER: Always isolate variables and then graph. x < -1 x > 1 x ≤ 0 x ≥ 2

22. VIDEOS: InequalitiesMultiplication/Division https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-division

23. CLASSWORK:Page 181-183 Problems: As many as needed to master the concept.