178 CHAPTER 3 Graphs, Linear Equations, and Functions
OBJECTIVE 3 Graph the union of two linear inequalities. When two
inequalities are joined by the word or,we must find the union of the graphs of the
inequalities. The graph of the union of two inequalities includes all of the points
that satisfy either inequality.
Graphing the Union of Two Inequalities
Graph or
The graphs of the two inequalities are shown in FIGURES 40(a) AND (b)in Example 3
on the preceding page. The graph of the union is shown in FIGURE 41.
2 x+ 4 yÚ 5 xÚ 1.
EXAMPLE 4
x
y
0
2 x + 4y ≥ 5
or x ≥ 1
FIGURE 41 NOW TRY
Recall from Section 3.3that the x-intercept of the graph of the line
indicates the solution of the equation We can extend this observation
to find solutions of the associated inequalities and
For example, to solve the equation
and the associated inequalities
and
we rewrite the equation so that the right side equals 0.
We graph
to find the x-intercept as shown in FIGURE 42.
The solution set of is
The graph of Y lies abovethe x-axis for x-values less than.
Thus, the solution set of is
The graph of Y lies belowthe x-axis for x-values greater than.
Thus, the solution set of - 213 x+ 12 6- 2 x+ 18 is 1 - 5, q 2.
- 5
- 213 x+ 12 7- 2 x+ 18 1 - q, - 52.
- 5
- 213 x+ 12 =- 2 x+ 18 5 - 56.
1 - 5, 0 2 ,
Y=- 21 3X+ 12 + 2X- 18
- 213 x+ 12 + 2 x- 18 = 0
- 213 x+ 12 7- 2 x+ 18 - 213 x+ 12 6- 2 x+ 18,
- 213 x+ 12 =- 2 x+ 18
mx+ b 70 mx+ b 6 0.
mx+ b= 0.
y=mx+b
CONNECTIONS
–10
- 10 10
10
Y = –2(3X + 1) + 2X – 18
FIGURE 42
NOW TRY
EXERCISE 4
Graph
3 x- 5 y 615 or x 7 4.
NOW TRY ANSWER
4.
x
y
0
45
–3
3 x – 5y < 15
or x > 4