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
*?>V??Vi?
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
V????>`?V????
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 TX 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 TX 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 TX 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
???TX????E???????TX?? E???????TX????E???X???¡ãn
X CM
S N D
&OR WHAT VALUES OF X IS THE AREA OF THE RECTANGLE GREATER THAN
THE PERIMETER
CM
*?>V??Vi?
3OLVING )NEQUALITIES WITH 6ARIABLES ON "OTH 3IDES
?? S X D X
?¡ã?xM? ?{¡ã?xM??{?¡ã?x??M? ??¡ã????v?????????????? ?
X CM
??T{?E?TX????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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