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:

Sales Process Earnings

$0

$2500

$5000

$7500

x y

Complete the table:

Sales Process Earnings

$0 0.05(0) + 825 $825

$2500 0.05(2500) + 825 $950

$5000 0.05(5000) + 825 $1075

$7500 0.05(7500) + 825 $1200

x 0.05x + 825 y

The equation describing Gretchen’s Total pay in terms of her sale is…

y = 0.05x + 825

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 + 825 < 2500

To solve this inequality, isolate x between the symbols

Solve the inequality:

1000 < 0.05x + 825 < 2500 -825 -825 -825

175 < 0.05x < 1675 0.05 0.05 0.05

3500 < x < 33500

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

3500 < x < 33500

Solve the inequality

3 2 11 17x Subtract 11

8 2 28x Divide by -2

Reverse BOTH symbols

8 2 28x Divide by -2

4 14x Graph the solution

4 14

To win a card game, Bryan needs to score below 20 or above 40. He currently has

a score of 12.

12 + x < 20 or 12 + x > 40

This is another type of compound inequality

Solve this inequality by isolating each x

12 + x < 20 or 12 + x > 40-12 –12 -12 -12

x < 8 or x > 28

Bryan needs to score less than 8 points or more than 28 points

Complete Activity 6e

Solve and graph inequalitiesSolve and graph compound

inequalitiesSolve problems using

inequalities