Chapter(1:(Equations(and(Inequalities(
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Class!Notes!and!Homework!Worksheets!
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Chapter(1:(Equations(and(Inequalities(
Assignment(Sheet(
Date(
(
Topic(
Course(Introduction(
Assignment(
1)(Sign(class(syllabus,(both(
student(AND(parent(
2)(Get(supplies(by(Monday(
3)(Download(suggested(iPad(
apps(
Homework(1.1(
Completed(
(
(
1.1:(Real(Numbers(
and(Operations(
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1.2:(Algebraic(
Expressions(and(
Models/(1.3:(Solving(
Linear(Equations(
Begin(Homework(1.2Q1.3(
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1.2:(Algebraic(
Expressions(and(
Models/(1.3:(Solving(
Linear(Equations(
1.4:(Rewriting(
Equations(and(
Formulas(
1.4:(Rewriting(
Equations(and(
Formulas(
Complete(Homework(1.2Q1.3(
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Homework(1.4(
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Homework(1.4(Day(2(
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1.1Q1.4(Review(
(
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QUIZ(1.1Q1.4(
1)(Chapter(Review(pg.(58(#1Q25(
odd(
2)(Chapter(Test(pg.(60(#1Q25(
odd(
NO(HOMEWORK(
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1.6:(Solving(Linear(
Inequalities(
Homework(1.6(
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1.7:(Solving(Absolute(
Value(Equations(and(
Inequalities(
1.7:(Solving(Absolute(
Value(Equations(and(
Inequalities(
Homework(1.7(
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1.1Q1.7(Review(
1)(Chapter(Review(pg.(58(#2Q26(
even(
2)(Chapter(Review(pg.(60(#(27Q
40(
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Chapter(1(EXAM(
NO(HOMEWORK(
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1.1##Real#Numbers#and#Number#Operations#
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The!Real!Number!System!
Create#a#Venn#Diagram#that#represents#the#real#number#system,#be#sure#to#include#the#
following#types#of#numbers:#real,#irrational,#rational,#integers,#wholes,#and#
natural/counting.#
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Properties!of!Real!Numbers!
Let$a,$b$and$c$be$real$numbers.$
Property$
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Commutative##
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Associative# #
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Identity#
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Addition$
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a!+!b!=!b!+!a! !
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(a!+!b)!+!c!=!a!+!(b!+!c)!
a!+!0!=!a!;!!0!+!a!=!a! !
Inverse#
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a!+!(-a)!=!0!
Distributive#Property#
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!
Identify$the$property$illustrated.$
a.)##14#+#7#=#7#+#14# #
!
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1
b.)## 5⋅ = 1 # #
5
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2 ⎛ 2⎞
e.)## + ⎜ − ⎟ = 0 # #
3 ⎝ 3⎠
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d.)##5#(#x#+#2)#=#5x#+#10#
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Multiplication$
a!·!b!=!b!·!a!
(ab)!·!c!=!a!·!(bc)!
a!·1!=!a!!,!!1!·!a!=!a!
1
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a ⋅ = 1 ; (a ≠ 0) !
a
a(b!+!c)!=!ab!+!ac!
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c.)##(5#+#3)#+#2#=#5#+#(3#+#2)$
f.)##1#·#5#=#5#
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Unit!Analysis!
$
English#Units# #
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1#ft#=#12#in#######################
1#yd#=#3#ft#
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1#mi#=#5280#ft##
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1#lb#=#16#oz# #
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1#gal#=#4#qt# #
##
Conversion#Reference#Table#
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Metric#Units# #
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English#/#Metric#Units#
1#m#=#100#cm###
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1#in#=#2.54#cm##############
1#cm#=#10#mm#
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1#mi#=#1.61#km#####################
1#kg#=#1000#g##
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10#km#=#6.2#mi##
#1#L##=##1000#mL#
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lb#=#454#g##
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1#L##=#1.057#qt#
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Try#the#following#conversions.#
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1.)$$$2.45$mi$=_____________$ft$$
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$3.)$$470$mi$=$_____________$km$
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5.)$$526$yds/sec$=$_____________$mi/hr$
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7.)$10$gal$=$_____________$$mL$$
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2.)$$36$g$=$_____________$kg$ $
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4.)$200$mi/hr$=$_____________$ft/sec#
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6.)$75.0$kg$=$_____________$$lbs.$
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8.)$1.43$kg/L$=_____________g/mL$
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1.1
Real Numbers and Number Operations Homework
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1.#
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2.#
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Give#an#example#of#a#number#that#is#both#a#rational#number#and#a#whole#number.#
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Give#an#example#of#a#number#that#is#both#an#integer#and#a#natural#number#
(counting#number).#
Give#an#example#of#a#number#that#is#a#rational#number,#but#NOT#an#integer.#
Name#the#property#illustrated#in#each#example#below:#
a)#
5(x + 7) = 5x + 35 #
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______________________________#
b)#
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(59 + 7) + 62 = 59 + (7 + 62) # #
______________________________#
c)#
10 i
1
=1#
10
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______________________________#
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3.8 + 1.2 + 2.7 = 1.2 + 3.8 + 2.7 #
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d)#
______________________________#
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e)#
387#+#0#=#387##
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______________________________#
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f)#
4(3)#=#3(4)# #
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______________________________#
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g)#
0#=#5#+#(\5)# #
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______________________________#
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5.#
Perform#the#following#conversions#using#conversion#factors.###Show#your#set#up.###
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# ##########86#inches#=#____#ft##################################5.17#lb/gal#=#_____#lb/qt##
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###########2.4#g/mL#=#____#lb/gal###############################3.4#km/hr#=#______#mi/hr#
Use#what#you#have#learned#about#conversion#factors#to#solve#the#following#application#
problems.#
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6.#
The#elevator#in#the#Washington#Monument#takes#75#seconds#to#travel#500#ft#to###
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the#top#floor.#What#is#the#speed#of#the#elevator#in#miles#per#hour?#
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7.#
When#you#drive#across#the#border#into#Quebec,#Canada,#all#the#speed#limit#signs#
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are#in#km/hour.###How#might#you#get#a#quick,#reasonable#approximation#of#the#
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equivalent#speed#in#mi/hour?#
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8.#
As#a#nurse,#you#must#determine#the#proper#dose#of#a#medication#for#your#patient#
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who#weighs#160#pounds.##The#amount#of#medication#is#20#mg/kg.##(mg#of#medication#
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per#the#patient’s#weight#in#kilograms)###How#many#milligrams#of#medication#would#
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be#a#proper#dose#for#your#patient?#
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9.#
A#blood#donor#gives#1#pint#of#blood#each#time#he#donates.##He#learns#from#the#
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American#Red#Cross#that#he#will#be#honored#at#a#special#dinner#for#outstanding#
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donors#for#his#lifetime#donation#of#6#gallons#of#blood.##How#many#times#has#he#
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donated#blood?###(There#are#2#pints#per#1#quart#of#any#liquid.)#
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1.2#Algebraic#Expressions#and#Models#&#1.3#Solving#Linear#
Equations#
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Order$of$Operations$$K$$PEMDAS#
1.)##Undo#grouping#symbols#–#parentheses,#absolute#value,#braces,#brackets#
2.)##Evaluate#any#exponents#/#powers#
3.)##Do#multiplication#and#division#as#they#appear#left#to#right#
4.)##Do#addition#and#subtraction#as#they#appear#left#to#right#
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Evaluate$
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1.#
\8#+#5(1#–#(\3))3#
###2.# (−3)4 # #
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Evaluate$
−3x 2 − 5x + 7 #when# x = −2 # #
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Simplifying$Algebraic$Expressions$$$$$$$$
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1.$
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5n 2 (n + 1) − 3n 3 − 2n $ $
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Solving$Equations$
1.#
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5(x − 2) = −4(2x + 7) + x #
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2.#
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3.#
# −34 #
2x 3 + 3x 2 + 27 when# x = −4 #
2[(3n + 1)2 − n] #
1
1
1
x+ = x− #
3
4
6
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3.#
2⎛
6⎞ 1
3x +
= (5x − 1) #
⎝
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5⎠ 5
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4.#
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1⎞
⎛2
x = 4⎜ x + ⎟ $
⎝
5
3
5⎠
6.#
−5(2x + 3) = 2(4 − 3x) − 4x #
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5.#
1⎞
⎛
6x + 2 − 4x = 3(2x + 1) − 2 ⎜ 2x + ⎟ #
⎝
2⎠
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Word$Problem$Practice$
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1.) Find#four#consecutive#even#integers#that#total#92.#
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2.) Find#three#consecutive#integers#such#that#if#the#sum#of#the#first#two#is#decreased#by#the#third,#
the#result#will#be#68.#
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3.) Find#three#consecutive#even#integers#such#that#twice#the#smallest#plus#three#times#the#largest#
will#equal#the#middle#integer#increased#by#82.#
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4.) Mrs.#Bunker#paid#her#$7.15#grocery#bill#with#a#ten\dollar#bill#and#asked#for#her#change#in#dimes#
and#quarters.#If#she#received#21#coins#in#change,#how#many#quarters#did#she#receive?#
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5.) 65#students#and#teachers#from#Penncrest#High#School#are#going#to#a#play.#Tickets#costing#$4#for#
teachers#and#$3.60#for#students#were#purchased#at#a#total#price#of#$244.#How#many#$4#tickets#
were#bought?#
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6.) A#stamp#collector#has#a#group#of#ten#cent,#fifteen#cent#and#twenty#cent#stamps#that#total#$4.75#in#
value.#If#he#has#twice#as#many#twenty\cent#stamps#as#ten#cent#stamps#and#three#fewer#fifteen#
cent#stamps#than#10#cent#stamps,#how#many#twenty#cent#stamps#does#he#have?#
1.2 and 1.3 Homework
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Evaluate#the#following#expressions.#
1.)## −(3) # #
2.)# −(−2)4 # #
3.)## −4 2 #
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4.)## (−2)4 #
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5.)# (5 − 2)3 ÷ 9 − 6 # #
6.)## ((3 − 1) ⋅ 2 + (−3))5 #
7.)## −12 − (−2)2 + (4 − 5)4 #
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8.)## x 2 − 4xy when x = −2 and y = −3 # #
9.)#### 6 − x 2 + x when x = −2 #
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Simplify#the#following#expressions.##
10.)## 5(n 2 + n) − 3(n 2 − 2n) # #
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11.)## 8(y − x) − 2(x − y) #
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Solve#the#following#equations.#
12.)## 6(2x − 1) + 3 = 6(2 − x) − 1 #
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13.)#5x#+#2##=#2(2x+1)#+#x#
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14.)## −5(2x + 3) = 2(4 − 3x) − 4x #
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15.)## x − = − x + #
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5⎞
2⎛6
7 ⎞ 17
⎛7
16.)## 2 ⎜ x − ⎟ = −2 #
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17.)# − ⎜ x − ⎟ =
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⎝5
3⎠
3⎝ 5
10 ⎠ 20
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18.)##Find#three#consecutive#integers#such#that#if#three#times#the#smaller#is##
#########decreased#by#the#sum#of#the#other#two,#the#difference#will#be#46.#
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19.)#Nancy#has#a#bag#of#coins#totaling#$3.60#in#value.#If#she#has#two#more#nickels#######
#########than#quarters,#and#twice#as#many#quarters#as#dimes,#how#many#of#each#coin##
#########does#she#have?#
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1.4#Rewriting#Equations#and#Formulas#
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Warm$up:$
Solve#the#equation#
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2 7
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3 2
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Example$1:#Solve##for#y:### 11x − 9y
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Example$2:#Solve##for#y:### 6x +
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y = 21#
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Example$3:#Solve##for#y.#### xy + 2x
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= −4 #
= 20 #
Solve$each#formula#for#the#indicated#or#underlined#variable.#
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a.)## P = 2l + 2w #
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A =π r2#
b.)#
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d.)# E = mc 2 #####(solve#for#m)# #
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g.)# F =
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Gm1m2
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r2
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e.)# F = C + 32 #
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h.)# I =
1
c.)## A = bh #####(solve#for#h)#
2
f.) S = C − rC ####(solve#for#C)#
E
#####(for#R)#
R+ r
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i.)# A = h (b1 + b2 ) #for#b2#
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k.)# S = 2WH + 2WL + 2LH #(for#H)#
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j.)#
1 1
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R R1 R2
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1.4##Homework:###Rewriting#Equations#and#Formulas#
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1.) A#=#P#+#Prt###(solve#for#t#)#
2.) PV#=#nRT###(solve#for#R)#
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3.)
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P1V1 P2V2
=
###(Solve#for# P2 )#
T1
T2
4.) S = V0 t −16t 2 ##(#Solve#for# V0 )#
1
5.) V = πr 2 h ###(Solve#for#h)#
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6.)
1 1 1
= + ####(Solve#for#b)#
f a b
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7.) P =
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R−C
####(Solve#for#R)#
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8.) S = 2πr 2 + 2πrH ###(Solve#for#H)#
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1.4#Homework#Day#2#
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1.6#Solving#Linear#Inequalities#
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Graph#the#following#inequalities:#
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############\#4#<#x## #
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5# ≥ #x# #
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“And”#inequalities.##These#are#also#known#as#UNIONS,#denoted#by#the#symbol#∪#
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x# ≥ #\3#and#x# ≤ #4#
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x#<#3#and#x# ≤ #6#
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“Or”#inequalities.##These#are#also#know#as#INTERSECTIONS,#denoted#by#the#symbol#∩#
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######x# ≥ #4##or##x# ≤ #0# #
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x##>##10###or###x# ≤ #6# #
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Solve$and$Graph:$
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1.)#\ 11 y − 9 ≥ 13 ##
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____________________________________________________#
2.)# 2 x + 1 ≤ 6 x − 1 #
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3.)# −12 < −3x − 3 < 15 #____________________________________________________#
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4.)# − 2 x + 7 ≤ 3 ##or### 3 x + 5 ≤ 2 ____________________________________________________#
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1.6#Homework##
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Match$the$inequality$with$its$graph.$
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1.)###$$x# ≥ #4### #
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2.)##x#<#4#
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4.)####x# ≥ #4#or#x#<#\4# #
5.)#\4# ≤ #x# ≤ #4# #
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3.)#–#4#<#x# ≤ #4#
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6.)##x#>#4#or#x# ≤ #\4#
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Determine$whether$the$given$number$is$a$solution$to$the$inequality.$
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7.)###### − x − 2 ≤ −4 ############Is#9#a#solution#to#this#inequality?#
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8.)####### −8 < x − 11 < −6 #######Is#5#a#solution#to#this#inequality?#
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Solve$the$inequality.$Then$graph$your$solution.$
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9.)##### 5 + x ≤ 6 ###########
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10.)######5#–#5x##>##4(3#–#x)#### #
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11.)###### −5 ≤ −n − 6 ≤ 0 ####
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12.)###### −8 <
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13.)###### 3x + 2 < −10 or 2x − 4 > −4 ####
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14.)###### 3n + 1 > 10 and
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15.)###### 2(x + 3) < 14 or − 5 − x < 1 ##
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1.7##Absolute#Value#Equations#and#Inequalities#
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Absolute$Value$Equations$
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General!Form:!!#
ax + b = c #
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The#solution#set#for#this#equation#can#be#found#by#solving#these#two#equations:#
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ax + b = c
ax + b = −c #
Example:#
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5x + 2 = 27 #
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Absolute$Value$Inequalities$
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ax + b ≥ c
ax + b ≤ c #
General!Form:#
ax + b > c ########or########## ax + b < c
######or######
#####or#######
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When#you#solve#any#inequality,#rewrite#the#inequality#as#an#equal#sign.##Break#the#equation#
down#into#two#“cases”,#and#solve#each#individually.##Plot#each#solution#on#a#number#line#and#
pick#a#test#point#to#plug#into#the#original#inequality.##Write#the#solution#set#using#set#
notation.#
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−3x + 4 ≥ 5 #
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4 x + 3 ≤ 7#
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Practice$Problems:$$
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1.)###### x − 3 = 2 ###########
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3.)###### −3x + 10 > 7 ## #
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2.)###### 2 x + 7 < 11 #
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4.)###### −x + 5 ≤ 6 #
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5.)##### 2 x − 1 − 4 ≥ 2 ############################################ #
#6.)#### 4 2 y − 7 + 5 < 9 #
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$ 2 x − 1 ≤ 0 ###############################################################10.)# $ x − 3 > 0 $
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1.7#Homework#
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Decide#whether#the#given#number#is#a#solution#to#the#inequality.#
8 − 2n = 2 ; n = − 5 #
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Solve#the#equation.#
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−3x + 5 = 7 ; x = 4 #
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Solve#the#inequality.##
7x + 5 < 23 #
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416 − x − 2 ≥ 38
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7 − 3x ≤ −14
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8 − 3n − 3 ≤ 15 # #
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Solve#for#x.#Assume#a!and#b#are#positive.#
x+a <b
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x + a ≥ a#
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