1. TODAY YOU WILL LEARN HOW TO SOLVE INEQUALITIES USING MULTIPLICATION AND DIVISION Solving Inequalities Using Multiplication & Division

2. 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

3. SOLVING INEQUALITIES USING DIVISION 3x ≤ 12 3 Translation: 3 times 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

4. SOLVE THE INEQUALITY. THEN GRAPH THE SOLUTION.

5. 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 on both sides reverse the inequality symbol.

6. 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 on both sides reverse the inequality symbol. -2.-2 k > 6 k > 6 MULTIPLYING AND DIVIDING INEQUALITIES BY A NEGATIVE NUMBER

7. 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.

8. YOU TRY: SOLVE AND GRAPH THE INEQUALITIES

9. EXIT TICKET Solve and graph the inequality: 8x < –24

10. 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.

11. 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?

12. 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