Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1

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
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