2. IE
3-1
Inequalities and Their Graphs
Copyright ? by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Vocabulary
Review
1. Cross out any points that are NOT solutions of the equation 25g 5 215.
16 12
8
4
0
4
2. Write two equations using 3, 13, and k.
8
12
16
IE An inequalityVoiscaabmualtahreymBautiilcdael rsentence that uses an inequality symbol to compare the values of two
expressions. You can use a number line to visually represent the values thianteqsuaatliistyfysyamnboinlsequality.
inequality (noun) in ee KWAL uh tee
PWRhOaBtLinEeMqu1a:DliieWtnfyienRqriIetuiTopaInrlNie:tGysAesInnyNmtiEnsbQetoqhUluetAaovlLcieItoTyrmbIiEaspSlaaermexapthtrheeesvmsailaoutneics?aol fstewnoteenxcpertehsasitounsse.s an
,, ., $, #,
a) all real nuEmxbamerpslexs:leTshsethmaanthoermeaqtiucaallsteont-e7nces 3 . 2, 5 1 7b,) 621le, sasndthxa2n a2 n#u4mber k is greater than 13
are inequalities.
x E Nonexamples: The mathematical sentences 4 1 4 5 8 and x 2 5 5 1 are not inequalities. They are equations.
c) v is greateUr stheaYnoourr eVqoucaalbtoul5ary
d) the quotient of k and 9 is greater than 2
Is 3. Where does each mathematical sentence belong? Write each inequality or equation in the correct box.
I
17 $ 5
3x 5 9
2x . 5
2(4) 5 8
8 , 3x
e) b is less than 4
Inequality
f) 3 less thEaqnuagtiiosnless than or equal to 17
g
g) all real n4u.mCboemrsplpetgereeaachteirnetqhuaanliotyrweiqthua,l ,t.o,1#.5, or $.
h) the sum of t and 7 is less than -3
z , 4, so 4
z
g $ 22 so 22
gt 7
Im , 7, so 7
m
Chapter 3
78
A solution of an inequality is any number that makes the inequality true. The solutions of the inequality ! < 5
are all real numbers x that are less than 5. You can evaluate an expression to determine whether a value is a
solution of an inequality.
PROBLEM 2: IDENTIFYING SOLUTIONS BY EVALUATING Is the number a solution of 2! + 1 > 3?
323
yes
a) -3
d 3 tl 3
61 3
57 3
b) -1
2fDt 3
21 173
I3
c) 1
247 153
2 173
373
d) Consider the numbers -1, 0, 1, and 3. Which are solutions of 13 - 7+ 6?
y y
Ij 13 C DEG
131 7 6
2016
o
13 76756
13 0 6 13 6
y
lj 13 747 6
13 716
y3137656
13 21 6
616
816
Determine whether each number is a solution of the given inequality.
e) 4/ - 6 10
i) 2
4216110
8 6110
2 10
ii) 0
463 6110
O 6210 6110
iii) 5
4G 6 10
20 6110 14110
f)
123 3
11
i) 0.5
6 5 211
05 211
11211
ii) 2
6232211
24 211 2211
g) /(/x- 3) < 54
m2 3mL 54
54k
i) -10
toffo 3 254
106133 54 s4
ii) 0
06033 54
0 54
iii) 4
644 2
24 211
21211
Noo
iii) 9
9 C9 3 254
q 6 254
54 s4
o
O
XE 2
PROBLEM 3: GRAPHING AN INEQUALITY Graph each inequality.
a) ! > -4
I9
b) 7 < 0
8 4ft e
c) 3 8
teepees
EE
d)
7
-
9 :
z 244 Cz 2 as
e jogs
e) ; < -4
f) < 2
g) -3 < = or f 3
h) 5.75 > ? or basis
92 o
2 o 20467
6 40 27
g to
PROBLEM 4: WRITING AN EQUATION FROM A GRAPH What inequality represents the graph?
a)
b)
az I
b L4
c)
XL 3
d)
d Zo
e)
2
f)
fL 7
g)
YES
h)
h L2
PROBLEM 5: WRITING REAL-WORLD INEQUALITIES What inequality describes the situation? Be sure to define a variable.
a)
b)
0
Let costofatrailride C 219.99
Lets legalspeed OE SES
Define a variable and write an inequality to model each situation.
c) The restaurant can seat at most 172 people.
PE Let fpeople
172
d) A person must be at least 35 years old to be elected President of the United States.
Letaage
35
e) A light bulb can be no more than 75 watts to be safely used in this light fixture.
Lethewatts
WEI
f) At least 475 students attended the orchestra concert Thursday night.
Lets students 52475
g) A law clerk has earned more than $20,000 since being hired.
Let e earnings
e
20,000
................
................
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