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

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?

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

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

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

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

Solve the inequality: 1000 < 0.05x < < 0.05x < < x < 33500

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

Solve the inequality Subtract 11 Divide by -2

Reverse BOTH symbols Divide by -2 Graph the solution 414

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

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

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