Chapter Nine:  Inequalities and Absolute Value

Take notes on the following topics.

Chapter Nine

Section 9.1

Section 9.2

Section 9.3

Section 9.4

Section 9.5

Section 9.6

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Section 9.6    Graphing Systems of Linear Inequalities 

(Examples provided by Prentice Hall)

 

Example 1		Solve this system by graphing: 3x + 2y > 6 and 4x + y <  4 Graph the boundary line 3x + 2y = 6 [which contains the points (0, 3) and (2, 0)]. Graph the boundary line 4x + y < 4 [which contains the points (0, 4) and (1, 0)]. The solution is the region that contains the point (–1, 6).
Example 2	Samuel does odd jobs on Saturdays. He earns anywhere from $3 to $5 an hour. He can't work more than 8 hours, and he always does more than 3 hours of work for his next-door neighbor. Write an inequality for each condition given in this situation and graph the inequalities. Let the x-axis represent hours worked and the y-axis represent money earned. Samuel earns between $3 and $5 an hour: 3x <  y < 5x. He works at least 3 hours and no more than 8 hours: 3 <  x < 8. Graph the lines y = 5x, y = 3x, x = 3, and x = 8. Shade the solution between the vertical lines, below y = 5x, and above y = 3x.

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