1. 4-3: Solving Inequalities Using Multiplication and Division Essential Question: What is the main difference between solving inequalities and solving equations using multiplication and division.

2. 4-3: Inequalities Using ● & ÷ You can multiply the same value to each side of an inequality, just like you did with equations. ◦ When you multiply both sides of an inequality by a positive number, the direction of the inequality sign stays the same ◦ When you multiply both sides of an inequality by a negative number, reverse the sign of the inequality.

3. 4-3: Inequalities Using ● & ÷ Example 1: Multiplying by a positive Solve x / 2 < -1. Graph the solution. ◦ x / 2 < -1 ◦● 2 ● 2 Multiply each side by 2 ◦ x < -2

4. 4-3: Inequalities Using ● & ÷ Your Turn ◦S◦S olve b / 4 > ½. Graph your solution. bb > 2 ◦S◦S olve d / 3 > 5 / 6. Graph your solution. dd > 2 ½

5. Example 2: Multiplying by a negative Solve - k / 4 > -1. Graph the solution. ◦ - k / 4 > -1 ◦● -4 ● -4 Multiply each side by -4 ◦ k < 4Flip the inequality

6. 4-3: Inequalities Using ● & ÷ Your Turn ◦S◦S olve -6 > - 1 / 5 w. Graph your solution. 330 < w

7. Solving inequalities is similar to solving with multiplication. If you divide by a negative number, flip the inequality. Example 1: Solve -5z > 25. Graph the solution. ◦ -5z > 25 ◦ ÷-5 ÷-5 Divide each side by -5 ◦ z < -5Flip the inequality

8. 4-3: Inequalities Using ● & ÷ Your Turn ◦S◦S olve -2t < -8. Graph your solution. tt > 4 ◦S◦S olve -3w > 12. Graph your solution. ww < -4

9. Example 4: Real-World Application ◦ The student council votes to buy food for a local food bank. A case of 12 jars of spaghetti sauce costs $13.75. What is the greatest number of cases of sauce the students can buy if they use at most $216 for this project?  Let c = the number of cases of sauce  13.75c < 216  ÷13.75 ÷13.75  c < 15.71 ◦ At most, they can buy 15 cases (they don’t have enough money to buy 16 cases)

10. 4-3: Inequalities Using ● & ÷ Your Turn ◦S◦S tudents in the school band are selling calendars. They earn $0.40 on each calendar they sell. Their goal is to earn more than $327. Write and solve an inequality to find the number of calendars they can sell and still reach their goal. 00.40c > 327 cc > 817.5 TThey need to sell at least 818 calendars

11. Assignment ◦ Worksheet 4-3 ◦ 1 – 45, odd problems