Chapter 1 - Expressions, Equations, and Functions

Question 1

Write a verbal expression for the algebraic expression:

   h - 7

Answer 1

Seven less than the number h

Question 2

Write an algebraic expression for the verbal expression:

5 less than 4 times a number

Answer 2

4n - 5

Question 3

A Christmas tree company charges $55 per Christmas tree and additional Christmas tree food is an extra 50 cents. If p is the number of Christmas tree food packets bought, which expression would give us the total amount spent at the Christmas tree company?

a. 55p + 50
b. 50p + 55
c. .50p + 55

Answer 3

c. .50p + 55

Question 4

Evaluate the expression:

6 to the 4th power
or
6^4

Answer 4

6 x 6 x 6 x 6

                              1,296

Question 5

Evaluate the expression:

7[42 - (5-3)^2]

Answer 5

7[42 - (5-3)^2]
            = 7[42 - (2)^2]
            = 7[42 - 4]
            = 7[40]
            = 280

Question 6

Evaluate 2n + (3y - 4) - 4m if:

n = 3
y = 5
m = 4

Answer 6

2n + (3y - 4) - 4m
         = 2(3) + (3[5] - 4) - 4(4)
         = 6 + (15 - 4) - 16
         = 6 + (11) - 16
         = 17 - 16
         = 1

Question 7

Evaluate 4(6-2) + 7 x (1/7). 
Name the property used in each step.

Answer 7

4(6-2) + 7 + (1/7)
= 4(4) + 1 Distributive Property
= 16 + 1 Substitution
= 17 Substitution

Question 8

Abby is getting a new puppy. She needs 4 things before she picks up the puppy:

Purina ProPlan Large Breed Puppy Food: $35
KONG Huggz Koala: $11
Food and Water Bowls: $39
Bully Sticks: $15

Find out how much these cost all together and name the properties used.

Answer 8

35 + 11 + 39 + 15
      = 35 + 15 + 39 + 11 Communicative
      = (35 + 15) + (39 + 11) 
Associative 
      = (50) + (50)
Substitution
      = 100
Substitution

Question 9

Evaluate 8 x 4 x 6 x 2 using the properties of numbers. Name the properties used in each step.

Answer 9

8 x 4 x 6 x 2
= 8 x 2 x 6 x 4 Communicative
= (8 x 2)(6 x 4) Associative
= (16)(24) Substitution
= 384 Substitution

Question 10

Use the distributive property to rewrite 8 x 65. Then evaluate.

Answer 10

8 x 65
= 8(70 - 5)
= 560 - 40
= 520

Question 11

Rewrite the expression using the distributive property. Then simplify.

8(11w + 4)

Answer 11

8(11w + 4)

= 88w + 32

Question 12

Simplify 11w + 4w - 5w

Answer 12

11w + 4w - 5w
= 15w - 5w
= 10w

Question 13

Use the expression four times the sum of 4w and 9 subtracted from the difference of 9w and 4 times 5

a. Write an algebraic expression for the verbal expression
b. Simplify the expression, and indicate the properties used

Answer 13

4(4w + 9) - 5(9w - 4)
= 16w + 36 - 45w - 20
= 29w + 16

Question 14

Find the solution set of the equation 4n + 11 = 19 if the replacement set is {2,4,6,8,10}

Answer 14

n 4n + 11 = 19 True or False?

2            4(2) + 11 = 19            True
4            4(4) + 11 = 19            False
6            4(6) + 11 = 19            False
8            4(8) + 11 = 19            False
10           4(10) + 11 = 19          False

Question 15

Solve 6(4 - 2) + 6(7-5)

Answer 15

6(4-2) + 6(7-5)
= 24 - 12 + 42 - 30
= 12 + 12
= 24

Question 16

Solve each equation.

12 - (6^2 - 4) + x = 12

Answer 16

12 - (6^2 - 4) + x = 12
             = 12 - (36 - 4) + x = 12
             = 12 - (32) + x = 12
             = -20 + x = 12
             = x = 32

Question 17

Solve 2(n +3) = 2(n + 4)

Answer 17

2(n + 3) = 2(n + 4)
2n + 6 = 2n + 8

No Solution

Question 18

Solve 2(5n + 5) = 10(n + 1)

Answer 18

2(5n + 5) = 10(n + 1)
10n + 10 = 10n + 10

n is equal to ALL REAL NUMBERS

Question 19

Abby pays $12 every year for the Backyard Poultry magazine subscription. She also buys Chickens magazine for $3 per magazine. Let t equal total cost and m be the number of magazines bought separately. Find out how much the total cost would be if she bought 12 magazines separately.

Answer 19

t = 3m + 12
t = 3(12) + 12
t = 36 + 12
t = 48

Question 20

Abby is buying balloons for her sisters birthday party. She bought regular and special balloons. A regular balloon costs 75 cents and a special ballon costs $2. Write an algebraic for regular balloons (r) and special balloons (s) and the total cost (t). Then identify the independent and dependent variables.

Answer 20

t = .75r + 2s

Independent Variable - # of balloons bought
Dependent Variable - total cost

Question 21

Determine whether {(1,3),(4,2),(1,2),(2,7)} is a function.

Answer 21

No, there is 2 of the same domain

Question 22

Determine whether {(2,4),(1,3),(3,5),(4,6)} is a function

Answer 22

Yes, because the x-values do not repeat

Question 23

There are 4 chickens. One lays 3 eggs a week, one lays 5 eggs a week, one lays 4 eggs a week, and one lays 6 eggs a week.

{(1,3),(2,5),(3,4),(4,6)}

Determine the domain and range.

Answer 23

Domain: {1,2,3,4}
Range: {3,5,4,6}

Question 24

Determine whether 3x + 3y = 6 is a function.

Answer 24

x 3x + 3y = 6 y

-2 3(-2) + 3y = 6 4 Yes
-1 3(-1) + 3y = 6 3
0 3(0) + 3y = 6 2
1 3(1) + 3y = 6 1
2 3(2) + 3y = 6 0

Question 25

For f(x) = 2x + 4, find each value

a. f(3)
b. f(-2)

Answer 25

a. f(3) = 2(3) + 4
= 6 + 4
f(3) = 10

b. f(-2) = 2(-2) + 4
= -4 + 4
f(-2) = 0

Question 26

For f(x) = -12x + 4x - 11, find the values

a. f(3)
b. f(-2)

Answer 26

a. f(3) = 12(3) + 4(3) + 11
           = 36 + 12 + 11
           = 48 +11
    f(3) = 59
b. f(-2) = 12(-2) + 4(-2) + 11
             = -24 -8 + 11
             = -32 + 11
    f(-2) = -21