Practice B LESSON Solving Inequalities with Variables on ...

Name

LESSON

3-5

Date

Class

Practice B

Solving Inequalities with Variables on Both Sides

Solve each inequality and graph the solutions.

1. 2x ªÒ 30 ªÅ 7x

2. 2k ªÒ 6 ªÍ 5k ªÓ 3

3. 3b ªÓ 2 ªÄ 2b ªÒ 1

4. 2 «¶ 3n ªÒ 7 «§ ªÏ 5n

5. 5s ªÓ 9 ªÍ 2 «¶ s ªÓ 6 «§

6. ªÓ3 «¶ 3x ªÒ 5 «§ ªÅ ªÓ5 «¶ 2x ªÓ 2 «§

7. 1.4z ªÒ 2.2 ªÏ 2.6z ªÓ 0.2

7p ªÓ __

1 ªÄ __

1p

8. __

8

4

2

Solve each inequality.

9. v ªÒ 1 ªÏ v ªÓ 6

10. 3 «¶ x ªÒ 4 «§ ªÄ 3x

11. ªÓ2 «¶ 8 ªÓ 3x «§ ªÅ 6x ªÒ 2

Write and solve an inequality for each problem.

12. Ian wants to promote his band on the Internet. Site A offers website

hosting for $4.95 per month with a $49.95 startup fee. Site B offers

website hosting for $9.95 per month with no startup fee. For how

many months would Ian need to keep the website for Site B to be less

expensive than Site A?

13. For what values of x is the area of the rectangle greater than

the perimeter?

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

a107c03-5_pr.indd 36

36

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Holt Algebra 1

12/6/05 2:03:38 PM

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3OLVING )NEQUALITIES WITH 6ARIABLES ON "OTH 3IDES

 --"

??x

??x

&ILL IN THE BLANKS TO SOLVE EACH INEQUALITY

X  X  



?X



?X

X 

Y 

n



?Y



 n



?{

N  

N  

?xN  ?n

N  



?Y  ?{

?Y

N

?

xN

?{

Y 

S  D  ?

S  D



?

X

3OLVE EACH INEQUALITY AND GRAPH THE SOLUTIONS

Y   S Y  D



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3OLVING )NEQUALITIES WITH 6ARIABLES ON "OTH 3IDES

 --"

 K  











N



N









  

  





  

x

??

{????

x

 S  



















  S N   D  N

B???



x





K???

 B    B  



?n ?n

?

K  

X?

N

?

?n



?{



Y

 X    X







N???{













          

 SS   D

  S X   D   S X   D

S? ??

X???x

3OLVE EACH INEQUALITY AND GRAPH THE SOLUTIONS

 X  X  

 B  

      

B

X???











            



 ??P  ??  ??P







 Z    Z  

B? ??

??

P??????

?

Z? ??

     















     



















   

)DENTIFY EACH INEQUALITY AS AN IDENTITY ALL REAL NUMBERS ARE SOLUTIONS

OR CONTRADICTION NO SOLUTIONS 

 

 A    A



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 CM

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 --"

??x

 P    P



S  ??



 S N   D  

 ??Y  



N  

 Z    Z  

 B      B

Z

&OR n USE THE TABLE AT RIGHT 4HE TABLE

GIVES THE POPULATIONS OF 4OLEDO /HIO AND

,EXINGTON +ENTUCKY DURING THE LAST THREE

53 #ENSUSES

 D

X  X  

 !SSUMING THE PATTERNS IN THE TABLE CONTINUE

WRITE AND SOLVE AN INEQUALITY TO FIND THE YEARS

IN WHICH THE POPULATION OF ,EXINGTON WILL BE

GREATER THAN THE POPULATION OF 4OLEDO



X  ????

????



  D

X



Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

AK4up.indd 59

X



X   SX   D

X  X  

!DD X TO BOTH SIDES

X





$IVIDE BOTH SIDES

BY 



DECREASED  PEOPLE EACH YEAR



$IVIDE BOTH SIDES

BY 



X

X



7RITE THE FIRST STEP YOU WOULD TAKE TO SOLVE EACH INEQUALITY IF YOU

WANTED TO KEEP THE VARIABLE POSITIVE

   Y

 Y

Y  

 P    P

   R  R

   Y

!DD X TO BOTH SIDES

  ???

X

???

.OTICE THAT IF YOU WANT TO HAVE THE

VARIABLE ON THE LEFT TO MAKE GRAPHING

SOLUTIONS EASIER YOU MAY STILL NEED

TO SWITCH THE INEQUALITY SIGN EVEN

IF YOU DID NOT MULTIPLY OR DIVIDE BY A

NEGATIVE NUMBER

     

$ISTRIBUTE

  X

2EVERSE THE SIGN



X

  X  









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$ISTRIBUTE

>``??Y????L?? ???`i?

>``??P????L?? ???`i?

>``??R????L?? ???`i?

3OLVE EACH INEQUALITY



C     S C   D

  S X   D

X    X

   A    A  

   Y
  


Y Y   FOR YEARS AFTER 

C??{

#OPYRIGHT ? BY (OLT 2INEHART AND 7INSTON

!LL RIGHTS RESERVED



????????????



X  

INCREASED  PEOPLE EACH YEAR

 7RITE AN EXPRESSION FOR THE POPULATION OF

,EXINGTON ANY NUMBER OF YEARS AFTER 



  S   X D  X  

????????????

X   T
X   E



,EXINGTON +9      

 !BOUT HOW MUCH DID THE POPULATION OF

,EXINGTON CHANGE EACH YEAR



#OLLECT THE VARIABLES ON THE RIGHT

??Y  

D



4OLEDO /(

 7RITE AN EXPRESSION FOR THE POPULATION OF 4OLEDO

ANY NUMBER OF YEARS AFTER 



3OLVE X   T
X   E

NO SOLUTIONS



 !BOUT HOW MUCH DID THE POPULATION OF 4OLEDO

CHANGE EACH YEAR .OTE .OT EACH DECADE




#OLLECT THE VARIABLES ON THE LEFT

 A     S A   D A

 ??

K



3OLVE X   T
X   E

NO SOLUTIONS



  S K   D  K  

B  



6ARIABLES MUST BE COLLECTED ON THE SAME SIDE OF AN INEQUALITY BEFORE THE INEQUALITY CAN BE

SOLVED )F YOU COLLECT THE VARIABLES SO THAT THE VARIABLE TERM IS POSITIVE YOU WILL NOT HAVE TO

MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER

 S    S

P  ??



X  ??





,i?i>V

3OLVING )NEQUALITIES WITH 6ARIABLES ON "OTH 3IDES

X X

X    X  

 ???



    

  S X   D  X

#OPYRIGHT ? BY (OLT 2INEHART AND 7INSTON

!LL RIGHTS RESERVED

3OLVE EACH INEQUALITY

ALL REAL NUMBERS



???T
X????E???????T
X?? E???????T
X????E???X???¡ãn

X   CM



  S N   D



 &OR WHAT VALUES OF X IS THE AREA OF THE RECTANGLE GREATER THAN

THE PERIMETER

 CM

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3OLVING )NEQUALITIES WITH 6ARIABLES ON "OTH 3IDES

 ?? S   X D  X  





?¡ã?xM? ?{¡ã?xM??{?¡ã?x??M? ??¡ã????v?????????????? ?

X CM

??T
{?E?T
X????E???X???

?X??????

?

X  ??





 )AN WANTS TO PROMOTE HIS BAND ON THE )NTERNET 3ITE ! OFFERS WEBSITE

HOSTING FOR  PER MONTH WITH A  STARTUP FEE 3ITE " OFFERS

WEBSITE HOSTING FOR  PER MONTH WITH NO STARTUP FEE &OR HOW

MANY MONTHS WOULD )AN NEED TO KEEP THE WEBSITE FOR 3ITE " TO BE LESS

EXPENSIVE THAN 3ITE !

P???¡ã?xP????? ?P???P??n???}?i>?i??? >??fn?

X  



7RITE AND SOLVE AN INEQUALITY FOR EACH PROBLEM

 &OR WHAT VALUES OF X IS THE AREA OF THE RECTANGLE

GREATER THAN THE AREA OF THE TRIANGLE

 X  



>????i>?????Li??

 *AY CAN BUY A STEREO EITHER ONLINE OR AT A LOCAL STORE )F HE BUYS

ONLINE HE GETS A  DISCOUNT BUT HAS TO PAY A  SHIPPING FEE !T

THE LOCAL STORE THE STEREO IS NOT ON SALE BUT THERE IS NO SHIPPING FEE

&OR WHAT REGULAR PRICES IS IT CHEAPER FOR *AY TO BUY THE STEREO ONLINE

??x



 V    V  

?`i?????

7RITE AND SOLVE AN INEQUALITY FOR EACH PROBLEM

,%33/.



3OLVE EACH INEQUALITY

  S Z   D  Z

?`i?????

#OPYRIGHT ? BY (OLT 2INEHART AND 7INSTON

!LL RIGHTS RESERVED



(OLT !LGEBRA 

#OPY ? BY (OLT 2INEHART AND 7INSTON

!LL S RESERVED

59

X? ????

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?



A???x

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Holt Algebra 1

4/27/06 1:50:04 PM

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