1. Writing Inequalities from Graphs

2. Definition An inequality is a mathematical statement formed by placing an inequality symbol between numerical or variable expressions.

3. Write an inequality…. n is a number less than -3 t is a temperature greater than 20º F p is a price less than $10 and more than $5 w is a weight greater than or equal to 120 pounds d is a distance less than or equal to 75 miles.

4. When is the outside temperature more than 100°F?

5. Write an inequality to represent the x -values that correspond to each range of y -values. y > 0

6. Write an inequality to represent the x -values that correspond to each range of y -values. y ≤ 0

7. Write an inequality to represent the x -values that correspond to each range of y -values. y < 3

8. Write an inequality to represent the x -values that correspond to each range of y -values. 0 < y < 3

9. A dance organization sponsors a few dances every week. The admission price to each dance is $4 for members and 6$ for nonmembers. Membership in the organization costs $20. When is the total cost for a nonmember more than the total cost for a member?

10. The park district charges $3.50 to use the pool for nonmembers and $2 to use the pool for members. It costs $30 to join the park district. When is the total cost of using the pool for a nonmember more than the cost for a member?

11. A Tale of One Trucker

12. Complete the following table to show how far Travis is from Dallas at each hour. Use your table and the graph to write an equation that expresses Travis’ distance d from Dallas, as a function of the elapsed hours h since he left Pecos.

13. Experience tells Travis that the worst-case scenario would drop his average speed to 45 mph. Travis’s best-case scenario is shown on the grid below. On these same axes, draw the graph of his distance from Dallas, based upon his assumption that he can maintain a 45 mph average speed throughout his trip. Write an equation for the line you drew in response to Question 4.

14. Travis can average anywhere from 45 mph to 60 mph, as the two previous graphs suggest. On the axes in the Question 4 graph, sketch the vertical line h = 3 and highlight the segment that gives all of his possible distances from Dallas three hours after Travis leaves Pecos. How far might Travis be from Dallas after three hours of travel? Write your answer as an inequality.

15. Travis can average anywhere from 45 mph to 60 mph, as the two previous graphs suggest. On the axes in the Question 4 graph, sketch the vertical line h = 5 and highlight the segment that gives all of his possible distances from Dallas five hours after Travis leaves Pecos. How far might Travis be from Dallas after five hours of travel? Write your answer as an inequality.

16. Homework