1. In this lesson… We will solve problems using inequalities. We will solve compound inequalities.

2. Gretchen earns a monthly salary of $825 per month, and a commission of 5% of her sales. She normally earns a total between $1000 and $2500 a month. What are her normal sales per month?

3. Complete the table: SalesProcessEarnings $0 $2500 $5000 $7500 xy

4. Complete the table: SalesProcessEarnings $0 0.05(0) + 825 $825 $2500 0.05(2500) + 825 $950 $5000 0.05(5000) + 825 $1075 $7500 0.05(7500) + 825 $1200 x0.05x + 825y

5. The equation describing Gretchen’s Total pay in terms of her sale is… y = 0.05x + 825 She normally earns between $1000 and $2500

6. We can write a compound inequality to find the amount of Gretchen’s sales per month 1000 < 0.05x + 825 < 2500 To solve this inequality, isolate x between the symbols

7. Solve the inequality: 1000 < 0.05x + 825 < 2500 -825 -825 -825 175 < 0.05x < 1675 0.05 0.05 0.05 3500 < x < 33500

8. Gretchen’s normal sales are between $3,500 and $33,500 3500 < x < 33500

9. Solve the inequality Subtract 11 Divide by -2

10. Reverse BOTH symbols Divide by -2 Graph the solution 414

11. To win a card game, Bryan needs to score below 20 or above 40. He currently has a score of 12. 12 + x 40 This is another type of compound inequality

12. Solve this inequality by isolating each x 12 + x 40 -12 –12 -12 -12 x 28 Bryan needs to score less than 8 points or more than 28 points

13. Complete Activity 6e  Solve and graph inequalities  Solve and graph compound inequalities  Solve problems using inequalities