3.4D Homework:Module 3 Review Name:
Period:
Readeachset of directionscarefully.You must show all of your work to earncredit.Be sureto write all fractionanswersin simplestform.Goodluck! yardwitha perimeter 1. Theneighbors havea triangular of 4y * 3x - 2.Whichof thefollowing couldbe side yard? lengths of the Circleallthatapply. 4 y - 2 x + 1 , 4 x- 4 , a n d2 x + 1 -4 + 2x- y,5y + 3x, and -2x + 2 6 - 2 x , - Y + 7 x , a n d5 y - 2 x - 8 3(x + y-1), -(2x-2),and x - y - 1
@
- r t ,-
3 x + 1 \,-3 (-2 y+ x + 2) , and2y + $
2. Model each expressionwith labeledAlqebratiles and then simolif a.4-3x*3 b.2x' 4x*2x-
Model:
RaNB
MfrR
@n ro0T3
Simplified expression :
Simplified expression :
Simplifiedexpression :
rl -Au 3. Namethe propertvto lustltveach Statement/Steps AlgebraPropertyto justifychangefrom one stepto another: 2x(1)+20 + 4x a.
2x+20+4x 2x+20+4x
b.
2x+4x+20 2x+4x+20 c.
(2x + 4x)+20
a Sde*tyfuap. oFM,^f{' b Eorn^,*4*;vc
c &wi*l;tc
&ddrhon
(2x+4x)+20 d.
2 x ( 1+ 2 ) * Z O 2 x ( 1+ 2 ) + Z O
e.
2x(3)+ 26 2x(3)+ 20
f
g.
(3)2x+ 20 (3)2x+ 20 6x+20
e &*bsl',[ulw (srr-rTrlif; &.$ t (stnmulalrw
tbl-l
sstbs{i[t: *., (s,*d fr dw)
SDUHSDMathA CollegePrep- StudentEdition
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plus$2.00tuberentalper hour.Writean expression 4 . The waterparkcharges$5.50for admission, using the produ.ct of two factorsto findhow muchth'ecostwill be for a groupof 5 peopleto stay at the waterpark and rgnttubesfor any nqmberof hours(represented by the variableh).
( 'fuzh)e
5 . De\cribe the similarities 6/nOdifferencesbetween:
and zm+ +m@n
+.+n@n
@n
3i
e ted (factored)form. Drawa modelusinglabeledAlgebratilesto
6 . Writeeach expressionin
r answer. a. 5m* 15
,o,^,X(X- 4
Rever$edistributedform:
For each expresstQn, firstwrite he factoredform by factoringout the GreatestCommonFactor,thenwrite two otherfactoredlnrmsof the Xpression. 20x*30 \ ,/ 3 0- 1 5 v 1 4 h 2- z g h a. (GCF) \ ./ a. (GCF) a. (GCF) b.'
,/\
c.
\
b. c.
b.
c.
8. Modeland solveeachequationbelow.Drawalgebratilesto model,showyouralgebraic transformations qlyqqr equations. to solve,and checkyoursolution.Us Key for Tiles:
[=r
=x
X
=-x
-1
Model/Draw the equation a. 5*2x=
Recordthe stepsusingAlgebra
-7
Checksolutionin the equation
5*2x=-7
6 + 2s:'1 -1 5
5+z(U)'.1 2r, -la 6+(tz7z'1
-a )*rJg
bnfr
fr*Il3rlg SDUHSDMathA CollegePrep- StudentEdition
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d'-.J
L
z
'
,/
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b . - 3 ( x - 2 ' ): 9
-3(x - 2):9
-gx+W9
*6*+lvz4 -l
ml fr6'J. lffiNf,f,fr ry iofl
*fre
n,f,.f, a
e/
4 r-v
vi-,
=
3#
-
'lo -l'
-bv. ?
- 3(t'r'q
--zGz>tQ
4-?
ffi
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-
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9. Studentswereaskedto solvethe equation;(2x+ 4) : 10. Eachstudentdescribed whattheirfirststep wouldbe to solvethe equation.Circlewhichstudent(s)describeda correctfirststep,then solvethe equationusingone of the correctfirststepsyou chose. a. Toby:Subtract4 frombothsidesof the equation. to distribute 1zx+ +). (6\Vario: Use multiplication )to \./ c. Andrea:Subtracti from bothsidesof the equation.
Solve) { z* + 4) = 1o
^2
(d.)ffnatt:Multiplyboththe I and the 10 by 2 to ctearthe fracrion. \./ e. Olivia:Divideboththe; and the 10 by 5 to clearthefraction. Choosethe equationthat accuratelyrepresentseach problem,then solve each problemusing inverse operations 10.Ashleywentto the store,bought3 dozeneggsand spenta totalof $3.39.How muc[ did eachdozeneggs cost? a.3*x:3.39 c. x- 3 = 3.39 o' = t'=n
O,=3.3e
f
11.Sofaswere on salefor 25o/ooff theiroriginalpriceof $a|0 What is now the sale priceof.eachsofa? a..75x=450 b. r-.25x=450 d. 450-.25=x /-")*=.75(450) \-/,
For #12-14:choose and define a variable for the unknown, write an equation to representthe problem situationusing that variable,and solve the equation. ple questto 1 2 .In I a survey,one trftn fifth Iof the 1e people ned preferredorangejuice to apple uice.lf 45 peoplepreferred oranqeiuice.h'owma totalpesbl6were questioned? Definevourvariable: Writeequation: Solveequation:
:? ' = fol*l th #
?eode nuc+'ortt
+*=1s
tue=15
6'h+'-y'E P'7+6
SDUHSDMathA CollegePrep- StudentEdition
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13.Ameliaboughttwo booksyesterday.The priceof one was 3 timesas muchas the priceof the other'.lf the sum of the priceswas $8.60,whatwas the priceof the cheaperbook Writeequation: Solveequation: Definevourvariable:
Thceheo-p(b"k wa+h'.rb
9'let bool6
tax.Whatwas the sellingpriceof the 14.ln astatewitha 5% salestax,a tennisracketcost$60.85,including racketbeforetax? (Roundto the hundredth Writeequation: Solveeouation: Definevourvariable:
f : raQl&t'?/toe
r *,4r
3 b7,t6
l.06(L hO.86
l,06( ,lt/.6
ffiffi
r:'€n1,,16
15.Use eachof the givensymbols,numbers,and a variable(w) to makethreeequivalent expressions. You can use each objectmorethan once.Statewhichpropertiesyou usedto changethe 2ndand 3'd expressionsfromthe firstone. . (multiplication -21 +7 3 symbol) a.
*rcv*rg
h/i ll Vaqrt)
b.
Propertyusedto changefrom a t o b )
c.
Propertyusedto changefrom b t o c )
belowis (are)equivalent to -iC-s'"+10): 16.Choosewhichexpression(s)
-|rto -sm) m-2 c. m+2
6)-z+r\{.
f\ e ) ; ( - 1 0 + 5 m) /)f. -;(5m - 10)
17.Foryourbirthdayparty,you planto buy 2 cupcakesfor eachguestand 6 additional cupcakesto haveas extras.The cupcakescost $2.50each.Writean algebraicexpressionto representhow muchmoneyyou'll spendon cupcakesif you invitex numberof guests.
Z.4o(zu+t) property.ls 1 8 .J a s o ntellsyou the expression-4y(72) can be expandedto -2By - 4yz usingthe distributive Explain., , he tt-l-,tl lt ()
SDUHSDMathA CollegePrep- StudentEdition
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19.You paida totalof $48.75for the jeans you'vebeenwanting.Theywere on salefor 25% offof their algebraicequationsyou coulduseto findthe originalpriceof thejeans. originalprice.Writetwo different to findthe originalcost.(lgnoretax.) Solveone of yourequations
1'tequation , {- - ,%*-="t-/r,_78 2noequation: Solution:
.76K = +8.*16
Ori/naleF* v'/es
.76v=W ,76
,1b
fiu6
x'b€
20. Stac! boughtd photoof herselfand hpr friendsthat measured6 incheswide.She wantedit to fit intoa biggerframe,so she had it enlargedby 20%.The new printstillwasn'tbig enough,so she enlargedthe new photoby another20%. Let p representthe widthof the twiceenlargedphotoand writean equationto representthe problem.What is the widthof the twiceenlargedphoto?
b+(.Qte =l4lt)='l-2@
'l
t'1,2,1 .zh,i) = l,uh.d -t = t,b1,,
21.
42->( = lq -L+7
-LIL
rx=-2=7
nn"*"r,23
r"or"."nX n:"k?"given? 22. Whichone ofthefo||owing equations Laylamustbe at her musicteacher'sstudioin 60 minutes.lf it takes15 minutesfor her to reachthe studio,how muchextratime does Laylahave? 5*x=60
b . 1 5- x : 6 0
SDUHSDMathA CollegePrep- StudentEdition
c. 15r = 60
o'* = uo
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