LearningExpress Skill Builders • CHAPTER 4
99
x
1
. To divide x
4
by x
1
, you just subtract 4 Ϫ 1, to
get x
3
. The equation is now (
ᎏ
x
y
3
ᎏ
)(
ᎏ
3
7
y
3
ᎏ
). We divide y
3
by y, to get y
2
in the numerator. (x
3
)(

ᎏ
3
7
y
2
ᎏ
) =
ᎏ
3x
7
3
y
2
ᎏ
.
6. a. First, subtract 4 from both sides of the equa-
tion 2x ϩ 4 ϽϪ12 to yield 2x ϽϪ16. Next, divide
everything by 2 to get x ϽϪ8.
7. c. Substitute Ϫ5 in for b in the given equation.
Thus, (
ᎏ
1
6
ᎏ
)(b
2
ϩ b) = (
ᎏ
1
6

ᎏ
)(Ϫ5
2
ϩ 5) ϭ
ᎏ
1
6
ᎏ
(25 Ϫ 5)
ϭ
ᎏ
1
6
ᎏ
(20) ϭ
ᎏ
2
6
0
ᎏ
ϭ
ᎏ
1
3
0
ᎏ
.
8. d. Put Ϫ2 in for x in the equation 3x
2
Ϫ 2x ϩ 5.

Thus, the equation becomes 3(Ϫ2)
2
Ϫ 2(Ϫ2) ϩ
5 ϭ 3(4) Ϫ (Ϫ4) ϩ 5 ϭ 12 ϩ 4 ϩ 5 ϭ 21.
9. d. If b is greater than 5, then you can write b Ͼ 5.
In order to compare this to b ϩ 3, just add 3 to
both sides of the inequality: b ϩ 3 Ͼ 5 ϩ 3, or b
+ 3 > 8. Thus, b ϩ 3 must be greater than 8.
10. a. (x ϩ 2)
2
ϭ 4x can be rewritten as (x Ϫ 2) (x Ϫ
2) ϭ 0. So you know that x Ϫ 2 ϭ0, or x ϭ2.
11. b. 5x Ϫ 6 ϭ 3x ϩ 16 can be simplified by first sub-
tracting 3x from both sides to yield 2x Ϫ 6 ϭ 16.
Now, you add both 6 to both sides to get 2x ϭ 22.
Dividing both sides by 2, you get x ϭ 11.
12. d. Replace every q with a 6 in the equation 5q Ϫ
q
2
to yield 5(6) Ϫ (6)
2
ϭ 30 Ϫ 36 ϭϪ6.
13. d. x
2
ϩ 2x Ϫ 15 ϭ 0 can be factored into two sets
of parentheses: (x ± ?)(x ± ?). Because the coeffi-
cient on the x
2
is 1, we know the missing num-
bers add to 2 (because the coefficient of x is 2) and

multiply to Ϫ15 (the lone number is Ϫ15). Thus,
the numbers are Ϫ3 and ϩ5. The equation is
equivalent to (x Ϫ 3)(x ϩ 5) ϭ 0. This means x
Ϫ 3 ϭ 0 and x ϩ 5 ϭ 0, or x ϭ 3 and x ϭϪ5,
respectively.
14. c. Ϫ5x Ϫ 5 ϭ 30 can be simplified by first adding
5 to both sides: Ϫ5x ϭ 35. Next, divide by Ϫ5 to
yield x ϭϪ7.
15. a. Divide both sides of Ϫ3x Ͻ 9 by Ϫ3, but be sure
to flip the sign! Thus, you get x ϾϪ3.
16. a. (8x
3
y)(2x
5
y
9
) can first be reduced to 16x
3
yx
5
y
9
.
If you have the same base, when multiplying
exponents, remember to just add the powers. For
the x terms, you add 3 ϩ 5 to get x
8
. Since y is the
same as y
1

, when you add the powers of the y terms
you get 1 ϩ 9, or y
10
. Thus, the final answer is
16x
8
y
10
.
17. c. The given equation is 9(P ϩ 1) ϾϪ2(ϪP ϩ
2.5). First, we distribute the 9 to get 9P ϩ 9 ϾϪ2
(ϪP ϩ 2.5). Next, we distribute the Ϫ2 and the
inequality becomes 9 P ϩ 9 Ͼ (Ϫ2 )(ϪP) ϩ
(Ϫ2)(2.5), or 9P ϩ 9 Ͼ 2P ϩ (Ϫ5), or 9P ϩ 9 Ͼ
2P Ϫ5. Now we subtract 2P from both sides to get
7P ϩ 9 ϾϪ5. Then, we subtract 9 from both sides
to get 7P ϾϪ14. Finally, divide by 7 to get P Ͼ
Ϫ2.
18. b. He starts with $20 but we have to subtract the
cost of the three psychology books and the cost
of the vocabulary book in order to figure out his
change. Three psychology books at $3.25 each
would be represented as 3 ϫ 3.25 or 3(3.25). We
have 20 Ϫ 3(3.25) Ϫ 5 ϭ C.
19. b. The expression 3x
2
Ϫ x Ϫ 2 ϭ 0 can be factored
into two sets of parentheses: (3x ± ?)(x ±?).
Because the coefficient on the x
2

is not 1, focus
your attention on the lone number, Ϫ2, which
indicates that the numbers you will stick in the
parentheses have a product of Ϫ2. The numbers
will be a combination of Ϫ1 and 2 or 2 and Ϫ1.
Because one set of parentheses has a 3x,placement
–ESSENTIAL PRACTICE WITH MATH–
CHAPTER 4 • LearningExpress Skill Builders
100
will matter and you have to just test out all com-
binations until one works. The working combi-
nation is (3x ϩ 2)(x Ϫ 1) ϭ 0. Next, you solve
for x.
(3xϩ 2) (x Ϫ 1) ϭ 0
3x ϩ 2 ϭ0 x Ϫ 1ϭ0
3x ϭϪ2 x ϭ 1
x ϭϪ
ᎏ
2
3
ᎏ
Only Ϫ
ᎏ
2
3
ᎏ
is listed as an answer choice.
20. d. B
2
ϩ 8B ϩ 12 ϭ 0 can be factored into two sets

of parentheses: (B ± ?)(B ± ?). Because the coeffi-
cient on the B
2
is 1, we know the missing num-
bers add to 8 (because the coefficient of B is 8) and
multiply to 12 (the lone number is 12). Thus, the
numbers are 6 and 2, and the equation is (B ϩ
6)(B ϩ 2) ϭ 0. Solving for B,we get:
(B ϩ 6 ) (B ϩ 2) ϭ 0
Bϩ6 ϭ0 B ϩ 2 ϭ0
B ϭϪ6 B ϭϪ2
21. a. Take the given equation, 2x
3
ϩ 8 ϭ 62, and sub-
tract 8 from both sides to yield 2x
3
ϭ 54. Next,
divide both sides by 2 to get x
3
ϭ 27. (x)(x)(x) ϭ
27, or x ϭ3.
22. d. Notice that all the answer choices are expressed
as fractions. That’s your clue that you need to find
a common denominator for these terms. The
denominators are 3, 10, and 5, so 30 would be a
great common denominator.To turn
ᎏ
3
x
ᎏ

into some-
thing over 30, you are multiplying top and bot-
tom by 10. This first term becomes
ᎏ
1
3
0
0
x
ᎏ
.Now
look at the second term,
ᎏ
1
3
0
x
ᎏ
. To turn this term into
something over 30, you’ll multiply top and bot-
tom by 3, yielding
ᎏ
3
9
0
x
ᎏ
. Next, to turn
ᎏ
2

5
x
ᎏ
into some-
thing over 30, multiply top and bottom by 6, and
you get
ᎏ
1
3
2
0
x
ᎏ
. The original expression (
ᎏ
3
x
ᎏ
) ϩ (
ᎏ
1
3
0
x
ᎏ
)
Ϫ (
ᎏ
2
5

x
ᎏ
) is now (
ᎏ
1
3
0
0
x
ᎏ
) ϩ (
ᎏ
3
9
0
x
ᎏ
) Ϫ (
ᎏ
1
3
2
0
x
ᎏ
) ϭ
ᎏ
3
7
0

x
ᎏ
.
23. c. Starting with 2x Ϫ y ϭ 4 and x ϩ y ϭ 8, rewrite
them as 2x Ϫ 4 ϭ y and 8 Ϫ y ϭ x. Substitute the
first expression into the second: 8 Ϫ 2(2x Ϫ 4) ϭ
x and solve for x; this yields 12 ϭ 3x or 4 ϭ x.
24. a. Substituting x ϭ 3 and y ϭϪ2 into the equa-
tion 5x
2
ϩ 2xy
3
we get: 5(3)
2
ϩ 2(3)(Ϫ2)
3
ϭ (5)(9)
ϩ (2)(3)(Ϫ8) ϭ 45 ϩ (6)(Ϫ8) ϭ 45 ϩ (Ϫ48) ϭ
Ϫ3.
25. c. When you substitute a ϭ 2, b ϭϪ1, and c ϭ
ᎏ
1
2
ᎏ
, into the expression
ᎏ
2a Ϫ
c
b ϩ 5
ᎏ

you get:
which simplifies to:
which equals:
10 divided by
ᎏ
1
2
ᎏ
is the same thing as 10 times 2,
which equals 20.
10
ᎏ
ᎏ
1
2
ᎏ
4 ϩ1 ϩ 5
ᎏᎏ
ᎏ
1
2
ᎏ
2(2) Ϫ (Ϫ1) ϩ 5
ᎏᎏ
ᎏ
1
2
ᎏ
–BASIC SKILLS FOR COLLEGE–
LearningExpress Skill Builders • CHAPTER 5

101
C
•
H
•
A
•
P
•
T
•
E
•
R
SUMMARY
This chapter gives you the chance to apply what you have
learned. Included are practice tests in grammar, writing, and
reading comprehension. As you complete the sections, you
should be able to find your strengths and weaknesses.
PRACTICE TESTS IN
GRAMMAR, WRITING,
AND READING
COMPREHENSION
5
5
CHAPTER 5 • LearningExpress Skill Builders
102
PRACTICE GRAMMAR TEST
AGREEMENT
There is an agreement error in each of the following sentences. Mark an SV to the left of the sentence if there is

a subject/verb error. Mark a PA to the left if there is a pronoun/antecedent error. Then try rewriting the sentence
correctly.
______ 1. It is unacceptable to clone a child because they would be treated as second class and not as a tradi-
tional being.
_____________________________________________________________________________
_____________________________________________________________________________
______ 2. By euthanizing terminally ill patients, doctors will be relieved of the time they spend treating these
patients, and he or she will have more time to spend with patients they can really cure.
_____________________________________________________________________________
_____________________________________________________________________________
______ 3. Many incidents of condensed air pollution has killed or hospitalized hundreds of people at a time.
_____________________________________________________________________________
_____________________________________________________________________________
______ 4. The principle of the issue is still over legalizing the right to help someone end their life.
_____________________________________________________________________________
_____________________________________________________________________________
______ 5. The author’s focal point throughout his arguments are that human cloning would diminish family
relationships.
_____________________________________________________________________________
_____________________________________________________________________________
______ 6. In conclusion, air and garbage pollution is a real problem for Americans.
_____________________________________________________________________________
_____________________________________________________________________________
–BASIC SKILLS FOR COLLEGE–
LearningExpress Skill Builders • CHAPTER 5
103
______ 7. The list of candidates for graduation include my name and my brother’s.
_____________________________________________________________________________
_____________________________________________________________________________
______ 8. My books and my calculator remains in the test room.

_____________________________________________________________________________
_____________________________________________________________________________
______ 9. Her problem are migraine headaches.
_____________________________________________________________________________
_____________________________________________________________________________
______ 10. Each of the episodes on ER and NYPD Blue is exciting.
_____________________________________________________________________________
_____________________________________________________________________________
SENTENCE STRUCTURE
There is a sentence fragment, fused sentence, or comma splice error in each sentence below. First, mark an SF for
sentence fragment, a FS for fused sentence, or a CS for comma splice to the left of the sentence. Then rewrite the
sentence correctly.
______ 1. The two-car family is common these days everyone wants an SUV and a sedan.
_____________________________________________________________________________
_____________________________________________________________________________
______ 2. Roses are not difficult to grow, they just need to be fed and pruned regularly.
_____________________________________________________________________________
_____________________________________________________________________________
______ 3. California often endures brush fires that are hard to put out, some have been burning for years.
_____________________________________________________________________________
_____________________________________________________________________________
–PRACTICE TESTS IN GRAMMAR, WRITING, AND READING COMPREHENSION–
CHAPTER 5 • LearningExpress Skill Builders
104
______ 4. Some villagers had never seen an automobile. Only knowing bicycles as a means of transportation.
_____________________________________________________________________________
_____________________________________________________________________________
______ 5. Environmentalists fear that once the Alaska oil fields are opened for exploration, wilderness will be
destroyed. With no guarantees that our energy crisis will have been helped in the process.
_____________________________________________________________________________

_____________________________________________________________________________
______ 6. Recent census figures indicate that there has been a dramatic increase in the number of men who
are single parenting their children, the mothers gave up custody during the divorce proceedings.
_____________________________________________________________________________
_____________________________________________________________________________
______ 7. Human cloning is just years if not months away do we fully understand the social consequences of
our research?
_____________________________________________________________________________
_____________________________________________________________________________
______ 8. Testing cosmetics by using helpless animals is cruel, there should be laws to protect against such abuse.
_____________________________________________________________________________
_____________________________________________________________________________
______ 9. Weather maps, graphs, charts, tables. All are confusing to read.
_____________________________________________________________________________
_____________________________________________________________________________
______ 10. Hurricanes are dangerous storms costing thousands of dollars to homeowners in repair costs each
year, Congress should pass more laws to help citizens in crises such as these.
_____________________________________________________________________________
_____________________________________________________________________________
–BASIC SKILLS FOR COLLEGE–