HW 3-1
Fill in the blank with the missing element. Name the property represented by the sentence.
1.
5(a  b)  ___ a  5b
2.
3  (5  6)  (3  5)  ____
3.
1
(____)  1
3
4.
ab  b ___
Name the property illustrated in each example below:
5.
2  2  0
6.
ax  bx  x(a  b)
7.
 9  0  9
8.
c(de)  c(ed)
9.
a(bc)  (ab)c
1. What property is illustrated by the statement c  (a  5)  (c  a)  5
(1) Commutative
(2) Associative
(3) Distributive
(4) additive inverse
2. When solving the equation, 4(3x 2  2)  9  8x 2  7 , Emily wrote 4(3x 2  2)  8x 2  16 as her
first step. Which property justifies Emily’s first step?
(1) Addition property of equality
(2) Commutative property of addition
(3) Multiplication property of equality
(4) Distributive property of multiplication over addition
3. Which equation illustrates the multiplicative inverse property?
(1) a  1  a
(2) a  0  0
1
a
(4) (a)(a)  a2
(3) a( )  1
14. Simplify the following expression and justify each step.
12  3(a  2b)  2a  3b  9  b
GIVEN
15. Evaluate the following using your calculator
16.
a)
50 ÷ [(4 • 5) - (36 ÷ 2)] =
__________
b)
3 • 2[4 + (9 ÷ 3)] =
__________
c)
2 + [48 ÷ (12 + 4)] =
__________
Which equation below represents an quadratic function?
(1) 4x 2  3  19
(3) 3x  7  25
x
(2) 5  125
(4) 12  2x  5
17. An example of an equation is
(1) 2x 2  4x  12
(2) x  6
(3) 2x  x 2  3
(4) 4(x  6)(x  2)
18. Which expression is equivalent to 3 3  3 4 ?
(1) 912
12
(3) 3
7
(2) 9
7
(4) 3
19. State the domain and range for the following graph.
HW 3-2
Solve equations.
1)
3
m  13  35
7
2)
 3m  6  30
3)
3m  ( m  1)  6m  1
4)
3m  5m  12  7m  88  5
5)
5t 45

4
2
6)
4(3x  5)  5x  2(x  15)
7)
4x
 3x  4  2(5x  3)
7
8)
 6x 
2
(2x  3)  42
5
9)
Which equation illustrates the commutative property of addition?
(1)
(2)
10)
x+y=y+x
3(x + 2) = 3x + 6
(3)
(4)
Which statement illustrates the additive identity property?
(1) 6 + 0 = 6
(2) –6 + 6 = 0
11)
(3 + x) + y = 3 + (x + y)
3+x=0
(3) 4(6 + 3) = 4(6) + 4(3)
(4) (4 + 6) + 3 = 4 + (6 + 3)
The perimeter of the rectangle shown is 41 centimeters. What is the value of x?
2x + 3
5x
12)
From 5x3 – 8x2 + x, subtract 7x3 + 3x2 – 10x
13)
Simplify:
(3x 8 y 3 )(8xy 5 )
14)
Simplify:
(x 3  8)(x 3  6)
HW 3-3
Solve the following
1.
2
1
(x  4) 
5
2
2. 3x  2 
3.
1 x

2 3
2
4
(x  5) 
3
9
4.
x 1 x 1
  
2 3 3 2
5.
x3
4
 (x  1) 
2
5
6.
x x
  12
2 4
HW 3-4
Solve and graph the following.
1)
x
x
 1
2
4
2)
3
 (x  4)  15
7
3)
4(2 – x)  -2x
4)
–2(x – 3) > 5(x – 9)
5)
Solve and graph the inequality
x
 3  2 . Write the solution using Interval
4
Notation.
6)
Solve and graph the inequality  2x  4  8 . Write the solution using Interval
Notation.
7)
Describe and correct the error in the problem below.

-7 -6 -5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
8)
Which property does 5  (x  1)  5  (1 x) illustrate?
(1) Associative
(2) commutative
9)
Given f(x)  5x 2  2x  8 , find f(-4)
10)
Which number is not an integer?
(1) -5
(3)
2
(2)
(4)
3
(3) distributive
36
0
11)
Which of the following is an irrational number?
3
(1) 0
(3)
4
(2) –6
(4) 5
12)
Which of the following relations is NOT a function?
(1) {(1, 2), (2, 4), (4, 7), (6, 10)}
(2) {(2, 3), (3, 3), (4, 6), (6, 6)}
(4) additive inverse
(3) {(5, 8), (6, 9), (7, 10), (5, 11)}
(4) {(1, 1), (2, 2), (3, 3), (4, 4)}
HW 3-5
1)
Pencils sell for $0.19 each. Torry wants to buy at least one but not more than 10
pencils and has $1.50 in his pocket. How many pencils can Torry buy?
2)
Nancy sells her handmade scarves at the yearly craft show. She has to pay $50
for her booth at the craft show. The cost for making all her scarves was $168.
She sold 15 scarves at $20 each. Did she make a profit? Justify your answer.
What is the fewest number of scarves that she can make to have a profit?
3)
4)
The length of a rectangle is 15 and its width is w. The perimeter of the rectangle
is, at most, 50. Which inequality can be used to find the longest possible width?
(1)
30  2w  50
(3) 30  2w  50
(2)
30  2w  50
(4) 30  2w  50
As a waiter at a restaurant, Joe earns $2.25 an hour plus tips. If he made $55 in
tips and his total earnings did not exceed $70, how many hours could he have
worked?
5)
6)
Johanna works as a sales person at an electronics store. She earns a base salary
of $400 each week plus a 10% commission on her total sales. Johanna did not
keep track of her sales last week, but her take home pay was $1380, find the
total number of sales she had for last week.
In a math class, two students were asked to go to the board to simplify the
following expression.
15 – 3[2 + 6(-3)]
Student A
Student B
15 – 3[2 + 6(-3)]
15 – 3[2 – 18]
15 – 3[-16]
12[-16]
-192
15 – 3[2 + 6(-3)]
15 – 3[2 – 18]
15 – 3[-16]
15 + 48
63
Which student arrived at an incorrect answer? Explain your reasoning
7)
Evaluate the expression  3x 2 y  4x when x = -4 and y = 2?
8)
What is the additive inverse of –4?
(1) 
(2)
1
4
1
4
(3) 4
(4) –4
HW 3-6
1)
Using the picture shown. A gas station charges $0.10
less per gallon of gasoline if a customer also gets a
car wash. What are the possible amounts (in gallons)
of gasoline that you can buy if you also get a car
wash and can spend at most $20.
Suppose that a car wash costs $9 and gasoline regularly costs $2.19 per gallon.
What are the possible amounts (in gallons) of gasoline that you can buy?
2)
Joel is saving money for a summer camp that costs $1800. He has already saved
$500. He has 14 more weeks to save the remaining balance. What are the
possible average amounts of money that Joel can save per week in order to
attend summer camp?
If Joel saves $60 a week will he have enough money to go? Explain your answer.
3)
A zookeeper is designing a rectangular habitat for swans, as shown. The
zookeeper needs to reserve 500 square feet for the first 2 swans and 125 square
feet for each additional swan.
20ft
50ft
What are the possible numbers of swans that the habitat can hold?
Suppose that the zookeeper increases both the length and width of the habitat
by 20 feet. What are the possible numbers of additional swans that the habitat
can hold?
4)
A gym is offering a trial membership for 3 months by discounting the regular
monthly rate by $50. Jason is considering joining the gym if the total cost of the
membership is less than $100. Which inequality can he use to find the possible
regular monthly rates that Jason is willing to pay?
(1)
(2)
5)
3x  50  100
3(x  50)  100
(3)
(4)
3x  50  100
3(x  50)  100
Given the function g(x)  x 2  2x  8 find the following:
a) g(-5)
b) domain
c) range
6)
Which expression represents “ 5 less than the product of 7 and x”?
(1) 7x – 5
(2) 7(x-5)
(3) 5 – 7x
(4) 7 + x – 5
HW 3-7
1)
Find two consecutive integers such that 4 times the larger exceeds 3 times the
smaller by 28.
2)
Find three consecutive even integers such that the sum of the smallest and twice
the second is 20 more than the third.
3)
A town is fencing in a rectangular field that is 200 feet long and 150 feet wide.
At $10 per foot, how much will it cost to fence the field? Describe and correct
the error that a student made in the problem below.
4)
The length of the second side of a triangle is 2 inches less than the length of the
first side. The length of the third side is 12 inches more than the length of the first
side. The perimeter of the triangle is 73 inches. Find the length of each side of
the triangle.
5)
The length of a rectangle is twice the width. If the length is increased by 4 inches
and the width is decreased by 1 inch, a new rectangle is formed whose
perimeter is 198 inches. Find the dimensions of the original rectangle.
6)
The number of times that Larry, Curly, and Jack have each won a dance contest
can be represented by three consecutive integers. Such that twice the sum of
the first and second integers increased by half the third is 57. Find the number of
times of them won.
HW 3-8
1)
Samantha needs to have at least $100 in her checking account to avoid a low
balance fee. Samantha has $247 in her account, and she makes withdrawals of
$20 per week. What are the possible numbers of weeks that Samantha can
withdraw money and avoid paying the fee?
2)
In a piggy bank on his dresser, Tom has a total of $2.85 in pennies and quarters. If
the number of pennies is 5 more than three times the number of quarters, how
many pennies and quarters does he have in his piggy bank?
3)
After a PTA Fun Night at school, the Water Fountain game had many coins at the
bottom. When the coins were counted, it was found that the number of dimes
was half the number of quarters, the number of nickels was 7 more than three
times the number of quarters, and there were 34 pennies. If the total in the
foutain was $18.69, how many of each coin were in the fountain.
4)
Maggie has been collecting nickels and dimes for 2 weeks, and she has a total
of $5.15. If she has 7 more nickels than she has dimes, how many of each coin
does she have?
5) John has four more nickels than dimes in his pocket, for a total of $1.25. Which
equation could be used to determine the number of dimes, x, in his pocket?
(1) 0.10(x  4)  0.05(x)  $1.25
(2) 0.05(x  4)  0.10(x)  $1.25
(3) 0.10(4x)  0.05(x)  $1.25
(4) 0.05(4x)  0.10(x)  $1.25
6)
Simplify:
9c 6 d3 e
54c 3 d5 e 7
7)
Simplify:
(a  3)(a4  5a  7)
8)
Officials in a town use a function, C, to analyze traffic patterns. C(n) represents
the rate of traffic through an intersection where n is the number of observed
vehicles in a specified time interval. What would be the most appropriate
domain for the function?
1
1
1
(1) {…, -2, -1, 0, 1, 2, 3, …}
(3) {0, ,1, 1 , 2, 2 }
2
2
2
(2) {-2, -1, 0, 1, 2, 3}
(4) {0, 1, 2, 3, …}
HW 3-9
1)
Steve’s pets world sells aquariums that are rectangular prisms. The volume V of
an aquarium is given by the formula V=Lwh where L is the length, w is the width,
and h is the height.
Solve the formula for h.
Use the rewritten formula to find the height of the
aquarium shown, which has a volume of 5850 cubic
inches.
In #’s 2-4 Solve for y in terms of x.
2)
x  7y  0
3)
5)
The formula for the volume of a pyramid is v 
3x  2y  18
of B and V?
1
VB
3
3V
(2) h 
B
(1) h 
6)
If w 
(3) h 
V
3B
(4) h  3VB
2x  y
, solve for y in terms of r, w, and y.
r
4)
4y  x  20  y
1
Bh . What is h expressed in terms
3
7)
A formula is expressed as D  a(2  kx). Express k in terms of D, a, and x.
8)
For the equation
9)
If k  am  3mx , solve for m in terms of a, k, and x
10)
Mr. Stanton asked his students to write an algebraic expression on a piece of
paper. He chose four students to go to the board and write their expression.
r
 x  w , solve for r in terms of w and x.
3
Robert wrote:
4(2x  5)  17
Meredith wrote:
3y  7  11z
Steven wrote:
9w  2  20
Cynthia wrote:
8  10  4  12
Which student wrote an algebraic expression? Explain your reasoning.
11)
A method for solving 5(x  2)  2(x  5)  9 is shown below. Identify the property
used to obtain each of the two indicated steps.