Title: Lesson 1–1
Author: Teri Willard
Last saved by: MHE

Lesson 2–7

Example 1  Dashed Boundary
Graph 5x – 3y < 6.

The boundary is the graph of 5x – 3y = 6. Since the inequality symbol is <, the boundary will be dashed. 

Now test the point (0, 0). The point (0, 0) is usually a good point to test because it results in easy calculations.

5x – 3y | < | 6 | Original inequality
5(0) – 3(0) | < | 6 | (x, y) = (0, 0)
0 | < | 6 | true

Shade the region that contains (0, 0).

Example 2  Solid Boundary
FUND–RAISING  The Peerless High School Student Council is planning a raffle. They have chosen two different types of prizes to purchase, games for $12 each and stuffed animals for $8 each.
a. Write and graph an inequality to describe the total cost of the prizes if the student council wants to spend no more than $204.

Let x be the number of games and let y be the number of stuffed animals. Since the student council can spend at most $204 for the raffle, use a ≤ symbol. 
Cost of games | and | cost of stuffed animals | are at most | $204
12x | + | 8y | | 204

Since the inequality symbol is ≤ , the graph of the related linear equation 12x + 8y = 204 is solid.

Test (0, 0). |
12x + 8y ≤ 204 | Original inequality
12(0) + 8(0)  204 | (x, y) = (0, 0)
0 ≤ 204 | true

Shade the region that contains (0, 0). Since the variables cannot be negative, shade only the part in the first quadrant.

b. If the student council wants to spend exactly $204, what number of each can they buy?

There are several possibilities. One is 15 games and 3 animals since 12(15) + 8(3) = 204.

Example 3  Absolute Value Inequality
Graph 2y + |x| ≥ 4.

Since the inequality symbol is ≥, the boundary is solid. Graph the equation. Then test (0,0).

2y + |x| ≥ 4 | Original inequality
2(0) + | 0 | ≥ 4 | (x, y) = (0, 0)
0 + 0 ≥ 4 | | 0 | = 0
0 ≥ 4 | false

Shade the region that does not include (0, 0).