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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