1. Warm Up Solve each equation. 1. –5a = 30 2. Graph each inequality. 5. x ≥ –10 6. x < –3 –6 –10 3.4.

2. Lesson 3.3 Solving Inequalities by Multiplying or Dividing ≥ < > ≤ Less than or equal to greater than greater than or equal to Less than

4. Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly Notice colored in circles ≤ is less than or equal to ≥ is greater than or equal to

5. Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly Notice open circles < is less than > is greater than

6. Solving Inequalities Using Multiplication x  -2 3 3 x  -6 Translation: x divided by 3 is greater than or equal to negative 2. The opposite of divided by 3 is Multiplying by 3. What you do on one side you do on the other! 3 3 Graph -204-4-6

7. Solving Inequalities Using Division 3x ≤ 12 3 Translation: 3times x is less than or equal to 12. The opposite of multiplying by 3 is divided by 3. What you do on one side you do on the other! 3 1 Graph 024-2-4 x ≤ 4

8. Solve the inequality. Then graph the solution.

9. Use the Box Method to solve Isolate the variable Determine the operation Use the inverse operation

10. Use the Box Method to solve Isolate the variable Determine the operation Use the inverse operation

11. Multiplying and Dividing Inequalities by a Negative Number Solve the inequality. 12 > -3m 4 < m Step1: solve for m -divide by -3 Step 2: reverse the inequality symbol -3 < 12 > -3m When multiplying or dividing by a negative number reverse the inequality symbol.

12. Multiplying and Dividing Inequalities by a Negative Number Solve the inequality. k < -3 Step1: solve for k -Multiply by -2 Step 2: reverse the inequality symbol > -2. When multiplying or dividing by a negative number reverse the inequality symbol. -2.-2 k > 6

13. Tell whether the operation reverses the sign of the inequality. 1) Multiply each side by -1 2) Multiply each side b 3) Divide each side by 4. 4) Divide each side by -5.

14. You try: Solve the Inequalities

15. Additional Example: Application $4.30 times number of tubes is at most $20.00. 4.30 p ≤ 20.00 Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy? Let p represent the number of tubes of paint that Jill can buy.

16. 4.30p ≤ 20.00 p ≤ 4.65… Since p is multiplied by 4.30, divide both sides by 4.30. The symbol does not change. Since Jill can buy only whole numbers of tubes, she can buy 0, 1, 2, 3, or 4 tubes of paint. Additional Example Continued Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy?

17. Lesson Quiz Solve each inequality and graph the solutions. 1. 8x < –24 x < –3 2. –5x ≥ 30x ≤ –6 3.x > 20 4. x ≥ 6 5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible numbers of shirts she can buy? 0, 1, 2, 3, 4, 5, 6, or 7 shirts