1 x a. you go to the store and buy jeans and shirts. each

Q3#Exam#(MP1%MP3)#is#5/5/15#•#IF#A#TOPIC#IS#NOT#ON#THIS,#YOU#DON’T#NEED#TO#WORRY#ABOUT#IT.#MAKE#SURE#YOU#CAN#ANSWER#ALL#OF#THESE#QUESITONS#AND#EXPLAIN!!!!#USE+EXTRA+PAPER.+*The#first+two#pages#of#this#review#are#the#most+important!!#Be#ready#to#explain#all#answers.#A.+ Solving+equations+step+by+step.+NO+DECIMALS.+Leave+your+final+answers+as+fractions.+

a.# ## # # b.# xxx213

41

+−=+ #

c.# 141

32

−=+ mm # # # # # # d.#232

31

−=+ mm #

#

B.+ Inequalities:+writing+and+solving.+Sketch+a+graph+to+help!!+AGAIN%%USE+EXTRA+PAPER!!+a. You go to the store and buy Jeans and Shirts. Each pair of jeans cost $8 and each shirt costs $4. If you did not spend more than $24, find three possible 3 possible solutions or combinations that were purchased.

b.# Marsha#is#buying#plants#and#soil#for#her#garden.#The#soil#cost#$4#per#bag,#and#the#plants#cost#$10#each.#She#wants#to#buy#at#least#5#plants#and#can#spend#no#more#than#$100.#Find#a#possible#combination.#

c.## A#school#has#a#budget#of#$250#per#classroom#to#buy#workbooks.#A#math#workbook#costs#$10,#and#a#science#workbook#costs#$12.#If#you#want#to#buy#12#math#workbooks,#what#is#the#maximum#number#of#science#workbooks#you#can#buy?#

C.+ Use+the+quadratic+formula+to+find+the+solutions.+Write+down+the+formula::+

a.# # # # c.# ## # # # #

b.# ## # d.# #D. Domain and range. State the domain and range of the functions. Use proper notation such as [ > x > ] or [ < x < ]

# # # # ###

Name: _____________________________________________________________________ Date: ___________________

Student Accessible – studentaccessible.com – Maya Khalil

Solving Multi-Step Equations a. Use the distributive property as needed. b. Combine like terms as needed. Solve the following equations. Show all steps and make sure to check your answer. 1) 𝟔𝒙 + 𝟕 = 𝟑𝒙 − 𝟏𝟏

2) 𝟏𝟐𝒙 − (𝟕𝒙 − 𝟔) = 𝟒𝟏

3) 𝟐(𝟓𝒙 − 𝟖) = −𝟔(𝒙 − 𝟖)

4) – 𝟐𝒙 − 𝟓 + 𝟒𝒙 = 𝟕 + 𝟔𝒙

5) 𝟗(𝟏𝟎𝒑 − 𝟐) = 𝟐𝟕

6) 𝟏 𝟒 (𝟏𝟐𝒙 + 𝟒) − 𝟏𝟒 = − 𝟏

𝟐 (𝟖𝒙 − 𝟏𝟔)

7) 𝟑 𝟓 + 𝟑 𝟏𝟎 𝒙 = 𝟒 𝟓 + 𝟐 𝟓 𝒙

8) 𝟗[𝟓 − 𝟐(𝒙 − 𝟏)] = 𝟐𝟏 + 𝟔(𝒙 + 𝟑)

9) 𝟏𝟖 = 𝟒(𝒙 − 𝟐) − (𝒙 − 𝟖) 10) 𝟐(𝒙 − 𝟔) + 𝟒 = 𝒙 − 𝟒(𝒙 + 𝟐)

©x d2Q0D1S2L RKcuptra2 GSRoYfRtDwWa8r9eb NLOL1Cs.j 4 lA0lllx TrCiagFhYtKsz OrVe4s4eTrTvXeZdy.c I RM8awd7e6 ywYiPtghR OItnLfpiqnAiutDeY QALlegpe6bSrIay V1g.N Worksheet by Kuta Software LLC

9)

2

x2 − 3

x − 15 = 5

{4,

−5

2}10)

x2 + 2

x − 1 = 2

{1, −3}

11)

2

k2 + 9

k = −7

{−1,

−7

2}12) 5

r2 = 80

{4, −4}

13)

2

x2 − 36 =

x

{

9

2, −4}

14)

5

x2 + 9

x = −4

{

−4

5, −1}

15)

k2 − 31 − 2

k =

−6 − 3

k2 − 2

k

{

5

2,

−5

2}16) 9

n2 =

4 + 7

n

{

7 + 193

18,

7 −

193

18 }

17)

8

n2 + 4

n − 16 = −

n2

{

−2 +

2 37

9,

−2 −

2 37

9 }18)

8

n2 + 7

n − 15 = −7

{

−7 + 305

16,

−7 −

305

16 }

-2-

Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com


9)

2

x2 − 3

x − 15 = 5

{4,

−5

2}10)

x2 + 2

x − 1 = 2

{1, −3}

11)

2

k2 + 9

k = −7

{−1,

−7

2}12) 5

r2 = 80

{4, −4}

13)

2

x2 − 36 =

x

{

9

2, −4}

14)

5

x2 + 9

x = −4

{

−4

5, −1}

15)

k2 − 31 − 2

k =

−6 − 3

k2 − 2

k

{

5

2,

−5

2}16) 9

n2 =

4 + 7

n

{

7 + 193

18,

7 −

193

18 }

17)

8

n2 + 4

n − 16 = −

n2

{

−2 +

2 37

9,

−2 −

2 37

9 }18)

8

n2 + 7

n − 15 = −7

{

−7 + 305

16,

−7 −

305

16 }

-2-


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Kuta Software - Infinite Algebra 1 Name___________________________________

Period____Date________________Using the Quadratic Formula

Solve each equation with the quadratic formula.

1)

m2 − 5

m − 14 = 0

{7, −2}

2)

b2 − 4

b + 4 = 0

{2}

3)

2

m2 + 2

m − 12 = 0

{2, −3}

4)

2

x2 − 3

x − 5 = 0

{

5

2, −1}

5)

x2 + 4

x + 3 = 0

{−1, −3}

6)

2

x2 + 3

x − 20 = 0

{

5

2, −4}

7)

4

b2 + 8

b + 7 = 4

{

−1

2,

−3

2}8)

2

m2 − 7

m − 13 = −10

{

7 + 73

4,

7 −

73

4 }

-1-


9)

2

x2 − 3

x − 15 = 5

{4,

−5

2}10)

x2 + 2

x − 1 = 2

{1, −3}

11)

2

k2 + 9

k = −7

{−1,

−7

2}12) 5

r2 = 80

{4, −4}

13)

2

x2 − 36 =

x

{

9

2, −4}

14)

5

x2 + 9

x = −4

{

−4

5, −1}

15)

k2 − 31 − 2

k =

−6 − 3

k2 − 2

k

{

5

2,

−5

2}16) 9

n2 =

4 + 7

n

{

7 + 193

18,

7 −

193

18 }

17)

8

n2 + 4

n − 16 = −

n2

{

−2 +

2 37

9,

−2 −

2 37

9 }18)

8

n2 + 7

n − 15 = −7

{

−7 + 305

16,

−7 −

305

16 }

-2-


USE THESE GRAPHS TO ANSWER QUESTIONS 1 – 12.

A

B

C

D

E

F

G

H

I

J

K

L


A

B

C

D

E

F

G

H

I

J

K

L


M

N

O

P

Q

R

S

T

U

V

W

X

#E.+ Using+and+interpreting+graphs:#

a. Find the average rate of change for 25≤t≤30. b. Interpret its meaning. c. Find the average rate of change for 0≤t≤10. d. Interpret its meaning. ###F.+Rate+of+change:+interpreting+graphs+and+understanding+their+meanings:#

##

#

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

_____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________

_____________________________________________________________________ _____________________________________________________________________

Quick Check

Mary Sue’s Exercise Run

8

7

6

5

4

3

2

1

2 4 6 8 10 12 14 16 18 20 22 24

Time (in minutes)

By interpreting the graph, we will be able to determine several aspects of Mary Sue’s exercise run.

1. During which time period did Mary Sue walk? ___________ 2. Using your new knowledge, explain how you determined which time period

displayed when she walked.

3. During which time period did Mary Sue probably stop? ____________________ 4. Using your new knowledge, explain how you determined that this was when she

stopped.

5. During which time period did Mary Sue run? __________________________ 6. During which time period did Mary Sue jog? __________________________ 7. Using your new knowledge, explain how you were able to determine when she was

running and when she was jogging. Justify your answer using math.

8. Based on the information on the graph above, PREDICT what you think the trend would be if we added four more minutes to the graph.

________________

Rules

1. If the ________________ or _________________________ is

_______________, then the line moves up when read from left to right.

2. If the ________________ or _________________________ is

_______________, then the line moves down when read from left to right.

3. If the ________________ or _________________________ is

_______________, then the line remains horizontal when read from left to right.

Let’s Practice!

Heart Rate during Aerobics

Hea

rt B

eats

per

Min

ute

120

110

100

90

80

70

60

50

40

30

20

10

5 10 15 20 25 30 35 40 45

Time Exercising (in minutes)

Using the graph, answer the following questions.

1. During which time period was the heart rate increasing? ______________________

2. Using math, determine the exact rate of change for the increase (warm-up).

a.+What+does++++8+<+X+14++mean+in+this+graph?+++b.+What+is+the+domain+and+range+of+this+function?+Include+units!+++c.+Find+the+rate+of+change+between+minutes+0+and+8+

d.+Find+the+rate+of+change+between+minutes+5+and+15.+++e.+What+is+the+domain+of+this+graph?+Include+units!+++f.+Find+the+rate+of+change+between+minutes+0+and+8+#

G.+ Graphing+Inequalities+a.#Graph#the#following#inequality:# #x#–#2y##>#–10# Then#list#ONE#solution.## # b.#Graph#the#solution#set#of#the#system#

####

H.+Determine+if+a+relation+is+a+function+or+not.+EXPLAIN+why+or+why+not.+If+the+relation+is+a+function,+list+the+domain+and+range.+++a.# # # # b.# # # # # # c.#

# # # # ##

I.+ Real#life#Quadratic#Functions:#find#Vertex#and#Xdintercepts;#interpret#their#meanings!!#

a. ##

b. ##

c. ##

Worked out by Jakubíková K. 4

Homework State the domain and range of each relation. Then determine whether each relation is a function

Graph each relation or equation and determine the domain and range.

Find each value if f(x) = − 5x + 2 and g(x) = -2x + 3.

7. f(3) 8. f(-4) 9. g ( −1 2) 10. f(-2) 11. g(-6) 12. f(m - 2) 13. Use the functions below to perform the following operations: f(x) = 2x g(x) = x – 2 h(x) = x2 k(x) = x/2 k(x) x f(x) g(x) - h(x)f(x) - k(x) h(x) + k(x) f(x) ÷ k(x) g(x) x h(x)

Practice:

Find the slope and y-intercept for each table, and then write an equation.

Worksheet Level 2: Writing Linear Equations Goals: I have mastered level 2 when I can: Write an equation given the slope and y-intercept Write an equation from a table

Write an equation in slope-intercept form for each table below. Show how you found the slope and y-intercept.

Determine if the table represents a linear relationship, if yes, write an equation in slope-intercept form.

Name Class Date

Prentice Hall Algebra 1 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

7

Multiple Choice

For Exercises 1–4, choose the correct letter.

1. What is the vertex of the parabola shown at the right?

A. (21, 0) C. (1, 24)

B. (0, 23) D. (3, 0)

2. Which of the following has a graph that is wider than the graph of y 5 3x2 1 2?

F. y 5 3x2 1 3 H. y 5 24x2 2 1

G. y 5 0.5x2 1 1 I. y 5 4x2 1 1

3. Which graph represents the function y 5 22x2 2 5?

A. B. C. D.

4. What is the order, from narrowest to widest graph, of the quadratic functions f (x) 5 210x2, f (x) 5 2x2, and f (x) 5 0.5x2?

F. f (x) 5 210x2, f (x) 5 2x2, and f (x) 5 0.5x2

G. f (x) 5 2x2, f (x) 5 210x2, and f (x) 5 0.5x2

H. f (x) 5 0.5x2, f (x) 5 2x2, and f (x) 5 210x2

I. f (x) 5 0.5x2, f (x) 5 210x2, and f (x) 5 2x2

Short Response 5. A ball fell off a cliff into the river from a height of 25 feet. Th e function

h 5 230t2 1 25 gives the ball’s height h above the water after t seconds. Graph the function. How much time does it take for the ball to hit the water?

9-1 Standardized Test PrepQuadratic Graphs and Their Properties

x

y

2

2

2

4

42

x

y

4

4 4x

y

2

4

2 2

xy

22 2

xy

4

4 4

Name Class Date


17

Multiple Choice


1. Which equation represents the axis of symmetry of the function y 5 22x2 1 4x 2 6?

A. y 5 1 B. x 5 1 C. x 5 3 D. x 5 23

2. What are the coordinates of the vertex of the graph of the function y 5 2x2 1 6x 2 11?

F. (3, 22) G. (3, 16) H. (23, 229) I. (23, 220)

3. What are the coordinates of the vertex of the graph of the function y 5 3x2 2 12x 1 3?

A. (22, 29) B. (2, 215) C. (2, 29) D. (3, 26)

4. Which graph represents the function y 5 3x2 1 12x 2 6?

F. G. H. I.

5. Which equation matches the graph shown at the right? A. y 5 8x2 1 2x 2 5

B. y 5 8x2 1 2x 1 5

C. y 5 2x2 1 8x 1 5

D. y 5 2x2 1 8x 2 5

Short Response 6. A golf ball is driven in the air toward the hole from an elevated tee with an

upward velocity of 160 ft/s. Its height h in feet after t seconds is given by the function h 5 216t2 1 160t 1 18. How long will it take for the golf ball to reach its maximum height? What is the ball’s maximum height?

9-2 Standardized Test PrepQuadratic Functions

x

y

4

2 424

4

8

8

x

y

8

24 26

8

16

16

x

y

8

42 62

8

16

16

x

y

4

2 424

4

8

8

x

y

8

28

2

16

46

16

Name Class Date


27

Multiple Choice


1. What is the solution of n2 2 49 5 0? A. 27 B. 7 C. 47 D. no solution

2. What is the solution of x2 1 64 5 0? F. 25 G. 8 H. 48 I. no solution

3. What is the solution of a2 1 17 5 42? A. 25 B. 5 C. 45 D. no solution

4. What is the side length of a square with an area of 144x2? F. 12 G. 12x H. 412x I. no solution

5. What is the value of b in the triangle shown at the right? A. 24 in. B. 4 in. C. 44 in. D. no solution

6. What is the radius of a sphere whose surface area is 100 square centimeters? Use the formula for determining the surface area of a sphere, S 5 4πr2, and 3.14 for π. Round your answer to the nearest hundredth.

F. 2.82 cm G. 5 cm H. 5.64 cm I. 125,600 cm

7. What is the value of z so that 29 and 9 are both solutions of x2 1 z 5 103? A. 222 B. 3 C. 22 D. 184

Extended Response 8. A ball is dropped from the top of a building that is 250 feet tall. Th e height h of

the ball in feet after t seconds is modeled by the function h 5 216t2 1 250. Round to the nearest tenth if necessary.

a. How long will it take for the ball to reach the ground? Show your work. b. How long will it take for the ball to reach a height of 75 feet? Show your

work.

9-3 Standardized Test PrepSolving Quadratic Equations

24 in.2

b

3b

4! − 3!! < 9#!!!!!!!!!!!!!!! + 3!! > 6##

J.+Evaluating+Functions+

a.# Evaluate+f(2)+for:++ +#

b.#if# and## ….#Evaluate:# f(d5),####g(d4),######f(2/3),######f(4/7),#####g(3/4)##

K.+ Finding+solutions+of+where+two+functions+equal+each+other.+

#

a.## # b.## # #######c.## #########d.## #

L.# Factor+Completely+

a.### #### # #b.# #

c.## # d.# #

M.+Isolate/Solve+for+the+following+variable:++

a.####Solve#for#y:#####5xy+n

2=−6

# # # # b.#Solve#for#F:###### #

c.#Solve#for##y:######## # # # d.# Solve#for/Isolate#z:# ## # # # # # # # ##

e.##Solve#for##l:####### ## # # # f.#Solve#for#a:#

#

N.#Solve+and+justify+each+steps+(write+the+property+that+was+used)!!#Write#the#justification#for#each#step#in#solving#this#equation:#

##O.+Solve+each+equation,+and+justify+each+step+(like+above)+

a.##### # # # b.# # # # c.##### #####

SYNTHETIC SUBSTITUTION Use synthetic substitution to evaluate thepolynomial function for the given value of x.

37. ƒ(x) = 5x3 + 4x2 + 8x + 1, x = 2 38. ƒ(x) = º3x3 + 7x2 º 4x + 8, x = 3

39. ƒ(x) = x3 + 3x2 + 6x º 11, x = º5 40. ƒ(x) = x3 º x2 + 12x + 15, x = º1

41. ƒ(x) = º4x3 + 3x º 5, x = 2 42. ƒ(x) = ºx4 + x3 º x + 1, x = º3

43. ƒ(x) = 2x4 + x3 º 3x2 + 5x, x = º1 44. ƒ(x) = 3x5 º 2x2 + x, x = 2

45. ƒ(x) = 2x3 º x2 + 6x, x = 5 46. ƒ(x) = ºx4 + 8x3 + 13x º 4, x = º2

END BEHAVIOR PATTERNS Graph each polynomial function in the table. Then copy and complete the table to describe the end behavior of the graph of each function.

47. 48.

MATCHING Use what you know about end behavior to match the polynomialfunction with its graph.

49. ƒ(x) = 4x6 º 3x2 + 5x º 2 50. ƒ(x) = º2x3 + 5x2

51. ƒ(x) = ºx4 + 1 52. ƒ(x) = 6x3 + 1

A. B.

C. D.

DESCRIBING END BEHAVIOR Describe the end behavior of the graph of thepolynomial function by completing these statements: ƒ(x) ˘ !!!? as x ˘ º‡ and ƒ(x) ˘ !!!? as x ˘ +‡.

53. ƒ(x) = º5x4 54. ƒ(x) = ºx2 + 1 55. ƒ(x) = 2x

56. ƒ(x) = º10x3 57. ƒ(x) = ºx6 + 2x3 º x 58. ƒ(x) = x5 + 2x2

59. ƒ(x) = º3x5 º 4x2 + 3 60. ƒ(x) = x7 º 3x3 + 2x 61. ƒ(x) = 3x6 º x º 4

62. ƒ(x) = 3x8 º 4x3 63. ƒ(x) = º6x3 + 10x 64. ƒ(x) = x4 º 5x3 + x º 1

y

x

x

y

y

x

y

x

334 Chapter 6 Polynomials and Polynomial Functions

As AsFunction

x ˘ º‡ x ˘ +‡ƒ(x) = º5x 3 ? ?

ƒ(x) = ºx 3 + 1 ? ?

ƒ(x) = 2x º 3x 3 ? ?

ƒ(x) = 2x 2 º x 3 ? ?

As AsFunction

x ˘ º‡ x ˘ +‡ƒ(x) = x 4 + 3x 3 ? ?

ƒ(x) = x 4 + 2 ? ?

ƒ(x) = x 4 º 2x º 1 ? ?

ƒ(x) = 3x 4 º 5x 2 ? ?

Algebra I Name: ____________________________

Function Notation Worksheet Hour: _________ Date: ______________ 1. Evaluate the following expressions given the functions below:

g(x) = -3x + 1 f(x) = x2 + 7 h xx

( ) =12

j x x( ) = +2 9

a. g(10) = b. f(3) =

c. h(–2) =

d. j(7) = e. h(a) f. Find x if g(x) = 16 g. Find x if h(x) = –2

h. Find x if f(x) = 23 i. CHALLENGE! (in other words, optional) g(b+c)

j. CHALLENGE! (also optional) f(h(x))

2. Translate the following statements into coordinate points:

a. f(–1) = 1 b. h(2) = 7

c. g(1) = –1

Algebra I Name: ____________________________

Function Notation Worksheet Hour: _________ Date: ______________ 1. Evaluate the following expressions given the functions below:

g(x) = -3x + 1 f(x) = x2 + 7 h xx

( ) =12

j x x( ) = +2 9

a. g(10) = b. f(3) =

c. h(–2) =

d. j(7) = e. h(a) f. Find x if g(x) = 16 g. Find x if h(x) = –2

h. Find x if f(x) = 23 i. CHALLENGE! (in other words, optional) g(b+c)

j. CHALLENGE! (also optional) f(h(x))

2. Translate the following statements into coordinate points:

a. f(–1) = 1 b. h(2) = 7

c. g(1) = –1

806.3.2 Practice

Given the equations below, what is the value of x when f(x) = g(x)?

1. f(x) = 5x – 5 g(x) = 4x + 7 2. f(x) = 8x – 2 g(x) = 12x – 6 3. f(x) = 4(x - 5) +2 g(x) = x + 3 4. f(x) = 3x + 16 g(x) = 7x 5. f(x) = 8x + 4 g(x) = 11 – 6x 6. f(x) = 11x +3 g(x) = 14x – 6 7. f(x) = 4(x – 5) - 5 g(x) = 2x + 7.4 8. f(x) = 6(2x + 11) g(x) = 9x + 33

9. f(x) =

21 (2x + 6)

g(x) = 4x – 12 10. f(x) = 3x – 1 g(x) = 13 – 4x 11. f(x) = 5(4x – 2) g(x) = -12x 12. f(x) = 100(x – 3) g(x) = 450 + 50x 13. f(x) = 4x + 8 g(x) = 9x – 27 14. f(x) = 2x + 6 g(x) = 4x – 12 15. f(x) = 7x + 8 g(x) = 4x + 38

806.3.2 Practice



9. f(x) =

21 (2x + 6)


806.3.2 Practice



9. f(x) =

21 (2x + 6)


806.3.2 Practice



9. f(x) =

21 (2x + 6)


806.3.2 Practice



9. f(x) =

21 (2x + 6)


©e q2Z0V1u25 8Kvuxtkah GSSoffptdw9aprHeH 8LeL9Cd.r k SAsl5lD crQiigXhytcsE RrneDsUezrZvLeNdd.y 3 lMsaldFez kwri8t8hG fIHndfriinGiNtHeP 9AIlSgoeFb8rpao T2F.X Worksheet by Kuta Software LLC

11)

3

b3 − 5

b2 + 2

b

b(

3

b − 2)(

b − 1)

12)

7

x2 − 32

x − 60

(

7

x + 10)(

x − 6)

13)

30

n2b − 87

nb + 30

b

3

b(

2

n − 5)(

5

n − 2)

14)

9

r2 − 5

r − 10

Not factorable

15)

9

p2r + 73

pr + 70

r

r(

p + 7)(

9

p + 10)

16)

9

x2 + 7

x − 56

Not factorable

17)

4

x3 + 43

x2 + 30

x

x(

x + 10)(

4

x + 3)

18)

10

m2 + 89

m − 9

(

m + 9)(

10

m − 1)

Critical thinking questions:

19) For what values of

b is the expressionfactorable?

x2 +

bx + 12

13, 8, 7, −13, −8, −7

20) Name four values of

b which make theexpression factorable:

x2 − 3

x +

b

Many answers. Ex: 0, 2, −4, −10, −18

-2-


Practice Problems

1. Solve ! " #$ &'# #

2. Solve ( " )**+

, &'# -

3. Solve . " /0

1 &'# 2

4. Solve ( " 3 4 5 4 6 &'# 5

5. Solve 7 " 8 9 : &'# :

6. Solve ; " <=>

? &'# 5

7. Solve @ " ABC &'# B

8. Solve 8 " ,DE,F

GDEGF &'# H?

9. Solve 3I 4 5H " 6 &'# H

10. Solve ; " <=>=J=1

* &'# 6

11. Solve K " 2MAB 4 AC 4 BCN &'# B

12. Solve ( " 2MA 4 BN &'# A

13. Solve ! " /

O &'# P

14. Solve )

Q" )

<4 )

> &'# &

15. Solve ; " -M1 4 #$N &'# $

16. Solve S " -#$ &'# #

17. Solve 3I 4 5 " 6 &'# 3

18. Solve K " 2P#C &'# C

19. Solve ; " 2P#? 4 2P#C &'# C

20. Solve H 9 H) " 8MI 9 I)N &'# I

21. Solve . " T=UV

? &'# B

22. Solve 3I 4 5H 4 6 " 0 &'# H

23. Solve 2 " X

YMZ 9 32N &'# Z

24. Solve )

\" )

\F4 )

\D &'# .

25. Solve ] " ^?.*`0

UU,bbb &'# c

26. Solve d " ebUV

fD &'# B

27. Solve g " )

?8h? &'# 8

28. Solve 5$ 9 2# " 25 &'# $

29. Solve K " . 9 #. &'# .

30. Solve @ " )

UPC?M3# 9 CN &'# #

31. Solve ; " )

?:3A &'# :

32. Solve jFkF

lF" jDkD

lD &'# 7)

33. Solve Z " mnFnD

1D &'# o

34. Solve )?1p

V" 2q &'# B

35. Solve ; " )

?5C &'# 5

36. Solve r " #s &'# s

37. Solve C " h$ 9 16$? &'# h

38. Solve 2 " )bbu

v &'# w

39. Solve ; " KM1 9 qcN &'# c

40. Solve q " ))

XM( 9 15N &'# (

41. Solve x " S. &'# S

42. Solve x " 86? &'# 6?

43. Solve Z " Ty

1 &'# A

44. Solve ; " 2P#? 4 2P#C &'# P

LITERAL EQUATIONS WORKSHEET

Solve for the indicated variable in the parenthesis.

1) P = IRT (T) 2) A = 2(L + W) (W)

3) y = 5x - 6 (x) 4) 2x - 3y = 8 (y)

5) x + y = 5 (x) 6) y = mx + b (b) 3

7) ax + by = c (y) 8) A = 1/2h(b + c) (b)

9) V = LWH (L) 10) A = 4πr2 (r2)

11) V = πr2h (h) 12) 7x - y = 14 (x)

13) A = x + y (y) 14) R = E (I) 2 l

15) x = yz (z) 16) A = r (L) 6 2L

17) A = a + b + c (b) 18) 12x – 4y = 20 (y) 3

19) x = 2y - z (z) 20) P = R - C (R) 4 N

SOLUTIONS BELOW

LITERAL EQUATIONS WORKSHEET

Solve for the indicated variable in the parenthesis.

1) P = IRT (T) 2) A = 2(L + W) (W)

3) y = 5x - 6 (x) 4) 2x - 3y = 8 (y)

5) x + y = 5 (x) 6) y = mx + b (b) 3

7) ax + by = c (y) 8) A = 1/2h(b + c) (b)

9) V = LWH (L) 10) A = 4πr2 (r2)

11) V = πr2h (h) 12) 7x - y = 14 (x)

13) A = x + y (y) 14) R = E (I) 2 l

15) x = yz (z) 16) A = r (L) 6 2L

17) A = a + b + c (b) 18) 12x – 4y = 20 (y) 3

19) x = 2y - z (z) 20) P = R - C (R) 4 N

SOLUTIONS BELOW

Practice Problems

1. Solve ! " #$ &'# #

2. Solve ( " )**+

, &'# -

3. Solve . " /0

1 &'# 2

4. Solve ( " 3 4 5 4 6 &'# 5

5. Solve 7 " 8 9 : &'# :

6. Solve ; " <=>

? &'# 5

7. Solve @ " ABC &'# B

8. Solve 8 " ,DE,F

GDEGF &'# H?

9. Solve 3I 4 5H " 6 &'# H

10. Solve ; " <=>=J=1

* &'# 6

11. Solve K " 2MAB 4 AC 4 BCN &'# B

12. Solve ( " 2MA 4 BN &'# A

13. Solve ! " /

O &'# P

14. Solve )

Q" )

<4 )

> &'# &

15. Solve ; " -M1 4 #$N &'# $

16. Solve S " -#$ &'# #

17. Solve 3I 4 5 " 6 &'# 3

18. Solve K " 2P#C &'# C

19. Solve ; " 2P#? 4 2P#C &'# C

20. Solve H 9 H) " 8MI 9 I)N &'# I

21. Solve . " T=UV

? &'# B

22. Solve 3I 4 5H 4 6 " 0 &'# H

23. Solve 2 " X

YMZ 9 32N &'# Z

24. Solve )

\" )

\F4 )

\D &'# .

25. Solve ] " ^?.*`0

UU,bbb &'# c

26. Solve d " ebUV

fD &'# B

27. Solve g " )

?8h? &'# 8

28. Solve 5$ 9 2# " 25 &'# $

29. Solve K " . 9 #. &'# .

30. Solve @ " )

UPC?M3# 9 CN &'# #

31. Solve ; " )

?:3A &'# :

32. Solve jFkF

lF" jDkD

lD &'# 7)

33. Solve Z " mnFnD

1D &'# o

34. Solve )?1p

V" 2q &'# B

35. Solve ; " )

?5C &'# 5

36. Solve r " #s &'# s

37. Solve C " h$ 9 16$? &'# h

38. Solve 2 " )bbu

v &'# w

39. Solve ; " KM1 9 qcN &'# c

40. Solve q " ))

XM( 9 15N &'# (

41. Solve x " S. &'# S

42. Solve x " 86? &'# 6?

43. Solve Z " Ty

1 &'# A

44. Solve ; " 2P#? 4 2P#C &'# P

©u W2r0G1Z21 nKNuDtHaW sSoodfVtBw8aOrle7 uL3LICu.N P gAslGlv 7rViogBh7t8sW ir8ejsCeWrRvkeBdm.Y d tMraedse0 cwqiPtxhl 1ISnbftiAnciYtueV dAolwgQembmrKas H1Y.4 Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 1 Name___________________________________

Period____Date________________Two-Step Equations

Solve each equation.

1) 6 =

a

4 + 2 2)

−6 +

x

4 = −5

3)

9

x − 7 = −74) 0 =

4 +

n

5

5) −4 =

r

20 − 5 6) −1 =

5 +

x

6

7)

v + 9

3 = 8

8)

2(

n + 5) = −2

9)

−9

x + 1 = −8010) −6 =

n

2 − 10

11) −2 =

2 +

v

4

12) 144 =

−12(

x + 5)

-1-

Example 3 Solve the equation 3x ! 6 = !1 and justify each step.

3x ! 6 = !1!!!!!!

3x ! 6 + (6) = !1+ (6)!

3x + 0 = 5

3x = 5

13!(3x) = 1

3(5)

1x = 53!

x =53

given

addition property of equality

additive inverses

additive identity

multiplication property of equality

multiplicative inverses

multiplicative identity

Problems

In problem 1 provide the justification for each step and in problems 2 through 9 solve the

equation and justify each step.

1. 2(x + 4) = !7

2x + 8 = !7

2x + 8 + !8 = !7 + !8

2x + 0 = !15

2x = !15

122x( ) = 1

2!15( )

1x = !152

x = !152= !7 1

2

given

a. ________________

b. ________________

c. ________________

d. ________________

e. ________________

f. ________________

g. ________________

2. !3x = 10 3. 7 + y = !3 4. x +2

3= 1

1

2

5. 3x + 2 = !7 6. !9 =1

2m + 3 7. !

2

3y = 5

8. !2x ! 6 = !7 9. 3 x ! 2( ) = !9 10. !5 =c!4

3

Answers (Justifications for problems 2 through 9 may vary.)

1a. distributive prop. 1b. (+) prop. of equal. 1c. (+) inverses 1d. (+) identity

1e. (x) prop. of equal. 1f. (x) inverses 1g. (x) identity 2. !10

3

3. –10 4. 5

6 5. –3 6. –24

7. !15

2 8. 1

2 9. –1 10. –11


3x ! 6 = !1!!!!!!

3x ! 6 + (6) = !1+ (6)!

3x + 0 = 5

3x = 5

13!(3x) = 1

3(5)

1x = 53!

x =53

given


additive inverses

additive identity




Problems



1. 2(x + 4) = !7

2x + 8 = !7

2x + 8 + !8 = !7 + !8

2x + 0 = !15

2x = !15

122x( ) = 1

2!15( )

1x = !152

x = !152= !7 1

2

given

a. ________________

b. ________________

c. ________________

d. ________________

e. ________________

f. ________________

g. ________________

2. !3x = 10 3. 7 + y = !3 4. x +2

3= 1

1

2

5. 3x + 2 = !7 6. !9 =1

2m + 3 7. !

2

3y = 5

8. !2x ! 6 = !7 9. 3 x ! 2( ) = !9 10. !5 =c!4

3




3

3. –10 4. 5

6 5. –3 6. –24

7. !15

2 8. 1

2 9. –1 10. –11


3x ! 6 = !1!!!!!!

3x ! 6 + (6) = !1+ (6)!

3x + 0 = 5

3x = 5

13!(3x) = 1

3(5)

1x = 53!

x =53

given


additive inverses

additive identity




Problems



1. 2(x + 4) = !7

2x + 8 = !7

2x + 8 + !8 = !7 + !8

2x + 0 = !15

2x = !15

122x( ) = 1

2!15( )

1x = !152

x = !152= !7 1

2

given

a. ________________

b. ________________

c. ________________

d. ________________

e. ________________

f. ________________

g. ________________

2. !3x = 10 3. 7 + y = !3 4. x +2

3= 1

1

2

5. 3x + 2 = !7 6. !9 =1

2m + 3 7. !

2

3y = 5

8. !2x ! 6 = !7 9. 3 x ! 2( ) = !9 10. !5 =c!4

3




3

3. –10 4. 5

6 5. –3 6. –24

7. !15

2 8. 1

2 9. –1 10. –11


3x ! 6 = !1!!!!!!

3x ! 6 + (6) = !1+ (6)!

3x + 0 = 5

3x = 5

13!(3x) = 1

3(5)

1x = 53!

x =53

given


additive inverses

additive identity




Problems



1. 2(x + 4) = !7

2x + 8 = !7

2x + 8 + !8 = !7 + !8

2x + 0 = !15

2x = !15

122x( ) = 1

2!15( )

1x = !152

x = !152= !7 1

2

given

a. ________________

b. ________________

c. ________________

d. ________________

e. ________________

f. ________________

g. ________________

2. !3x = 10 3. 7 + y = !3 4. x +2

3= 1

1

2

5. 3x + 2 = !7 6. !9 =1

2m + 3 7. !

2

3y = 5

8. !2x ! 6 = !7 9. 3 x ! 2( ) = !9 10. !5 =c!4

3




3

3. –10 4. 5

6 5. –3 6. –24

7. !15

2 8. 1

2 9. –1 10. –11

1 x a. you go to the store and buy jeans and shirts. each

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