Lesson 1-8

Example 1
Graph each inequality.

a.	x < 4
The boundary is not included in the graph. So the vertical line  should be a dashed line.

Testing (0, 0) in the inequality yields a true inequality, 0 < 4. So shade the half plane that includes (0, 0).
		
b.	x - 4y - 8  0
		
	The graph does include the boundary. So the line is solid.

Testing (0, 0) in the inequality yields a false inequality, so shade the half plane that does not include (0, 0).
		
c.	y > |x - 3|
Graph the equation  with a dashed boundary.

Testing (0, 0) yields the false inequality 0 > 3, so shade the region that does not include (0, 0).		

Example 2
FITNESS  Laurie follows a daily exercise program in which that she spends part of her time running on a treadmill at a rate of 7.0 miles per hour, and the rest of her time doing weight training. Doing so, she burns about 800 calories per hour on the treadmill, and about 200 calories per hour lifting weights.

a.	Draw a graph that models the combinations of time that Laurie can spend running on the treadmill and lifting weights in order to burn between 1000 and 1200 calories in a day.

Let x represent the number of hours Laurie spends running on the treadmill and y represent the number hours she spends lifting weights. She wants to burns at least 1000 calories each day, but no more than 1200 calories. Write an inequality.

1000  800x + 200y  1200
You can write the compound inequality as two inequalities, 1000  800x + 200y and
800x + 200y  1200. Solve each part for y.

	and			
Graph each boundary line and shade the appropriate region. The graph of the compound inequality is the area in which the shading overlaps.		

b.	Name three ways that Laurie can combine her time running on the treadmill and lifting weights in order to burn her target number of calories.

Any point in the shaded region or on the boundary lines meets the requirements. Three possible combinations are (0.5, 3.5), (0.75, 2.5), and (1.0, 1.5). These ordered pairs represent 30 minutes running and 3.5 hours weight lifting, 45 minutes running and 2.5 hours weight lifting, and 1.0 hours running and 1.5 hours weight lifting.