Since 1 ... 6 is true, shade the region containing the test point 1 1, 3 2 .See FIGURE 39.
SECTION 3.5 Graphing Linear Inequalities in Two Variables 227
xy(1, 3)036x = 2y
x ≤ 2 yFIGURE 39cannot be used
as a test point.1 0, 0 2NOW TRYGraphing calculators have a feature that allows us to shade regions in the plane,
so they can be used to graph a linear inequality in two variables. The calculator will
not draw the graph as a dashed line, so it is still necessary to understand what is and
what is not included in the solution set.
To solve the inequalities in one variable, and we
use the graph of
in FIGURE 40. For we want the values of xsuch that so
that the line is abovethe x-axis. From FIGURE 40, we see that this is the case for
Thus, the solution set is Similarly, the solution set of
is because the line is belowthe x-axis when
For Discussion or Writing
Use a graphing calculator to solve the following inequalities in one variable from
Section 2.8.
1. (Example 4, page 156)
2. (Use the result from part (a).)
3. 463 x- 5 ... 10 (Example 8(a), page 158)
3 x+ 2 - 5 6-x+ 7 + 2 x
3 x+ 2 - 5 7-x+ 7 + 2 x
y=- 2 x+ 46 0 1 2, q 2 , x 7 2.
x 6 2. 1 - q, 2 2.
y=- 2 x+ 47 0, y 7 0,
y=- 2 x+ 4
- 2 x+ 470 - 2 x+ 46 0,
CONNECTIONS
10–10- 10 10
FIGURE 40NOW TRY ANSWER
4.
xy0y Ä –2xComplete solution available
on the Video Resources on DVD
3.5 EXERCISES
Concept Check The following statements each include one or more phrases that can be
symbolized with one of the inequality symbols In Exercises 1–6, give the
inequality symbol for the boldface italic words.
1.Since it was recognized in 1981, HIV/AIDS has killed more than25 million people world-
wide and infected more than60 million, about two-thirds of whom live in Africa. (Source:
The President’s Emergency Plan for AIDS Relief, February, 2008.)
2.The average national automobile insurance premium of $1896 in 2007 was $20 less than
the 2006 average premium. (Source:2007 Mid-Year Auto Insurance Pricing Report.)6 , ..., 7 , or Ú.NOW TRY
EXERCISE 4
Graph .y...- 2 x