Because the coeffi-cient on the x2is 1, we know the missing num-bers add to 2 because the coefficient of x is 2 and multiply to 15 the lone number is 15.. Because the coefficient on the
Trang 1x1 To divide x4by x1, you just subtract 4 1, to
get x3 The equation is now (x y)(3 37y) We divide y3 3
by y, to get y2in the numerator (x3)(37y) = 2 3x73.y2
6 a First, subtract 4 from both sides of the
equa-tion 2x 4 12 to yield 2x 16.Next,divide
everything by 2 to get x 8
7 c Substitute 5 in for b in the given equation.
Thus, (16)(b2 b) = (16)(52 5) 16(25 5)
16(20) 260130.
8 d Put 2 in for x in the equation 3x2 2x 5.
Thus, the equation becomes 3(2)2 2(2)
5 3(4) (4) 5 12 4 5 21
9 d If b is greater than 5, then you can write b 5
In order to compare this to b 3, just add 3 to
both sides of the inequality: b 3 5 3, or b
+ 3 > 8 Thus, b 3 must be greater than 8.
10 a (x 2)2 4x can be rewritten as (x 2) (x
2) 0 So you know that x 2 0, or x 2
11 b 5x 6 3x 16 can be simplified by first
sub-tracting 3x from both sides to yield 2x 6 16
Now, you add both 6 to both sides to get 2x 22
Dividing both sides by 2, you get x 11
12 d Replace every q with a 6 in the equation 5q
q2to yield 5(6) (6)2 30 36 6
13 d x2 2x 15 0 can be factored into two sets
of parentheses: (x ± ?)(x ± ?) Because the
coeffi-cient on the x2is 1, we know the missing
num-bers add to 2 (because the coefficient of x is 2) and
multiply to 15 (the lone number is 15) Thus,
the numbers are 3 and 5 The equation is
equivalent to (x 3)(x 5) 0 This means x
3 0 and x 5 0, or x 3 and x 5,
respectively
14 c.5x 5 30 can be simplified by first adding
5 to both sides:5x 35 Next, divide by 5 to yield x 7
15 a Divide both sides of3x 9 by 3, but be sure
to flip the sign! Thus, you get x 3
16 a (8x3y)(2x5y9) can first be reduced to 16x3yx5y9
If you have the same base, when multiplying exponents, remember to just add the powers For
the x terms, you add 3 5 to get x8 Since y is the same as y1, when you add the powers of the y terms
you get 1 9, or y10 Thus, the final answer is
16x8y10
17 c The given equation is 9(P 1) 2(P 2.5) First, we distribute the 9 to get 9P 9 2 (P 2.5) Next, we distribute the 2 and the
inequality becomes 9 P 9 (2 )(P)
(2)(2.5), or 9P 9 2P (5), or 9P 9
2P 5 Now we subtract 2P from both sides to get 7P 9 5 Then, we subtract 9 from both sides
to get 7P 14 Finally, divide by 7 to get P
2
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 3.25 or 3(3.25) We have 20 3(3.25) 5 C
19 b The expression 3x2 x 2 0 can be factored into two sets of parentheses: (3x ± ?)(x ± ?) Because the coefficient on the x2is not 1, focus
your attention on the lone number,2, which indicates that the numbers you will stick in the parentheses have a product of2 The numbers will be a combination of1 and 2 or 2 and 1
Because one set of parentheses has a 3x, placement
Trang 2CHAPTER 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 2)(x 1) 0 Next, you solve
for x.
x 23
Only 23is listed as an answer choice
20 d B2 8B 12 0 can be factored into two sets
of parentheses: (B ± ?)(B ± ?) Because the
coeffi-cient on the B2is 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
6)(B 2) 0 Solving for B, we get:
B6 0 B 2 0
B 6 B 2
21 a Take the given equation, 2x3 8 62, and
sub-tract 8 from both sides to yield 2x3 54 Next,
divide both sides by 2 to get x3 27 (x)(x)(x)
27, or x3
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 3xinto
some-thing over 30, you are multiplying top and
bot-tom by 10 This first term becomes 1300 Nowx
look at the second term,130x To turn this term into
something over 30, you’ll multiply top and
bot-tom by 3, yielding 390x Next, to turn 25xinto
some-thing over 30, multiply top and bottom by 6, and
you get 1320 The original expression (x 3x) (130x)
(25x) is now (1300) (x 390x) (1320) x 370x
23 c Starting with 2x y 4 and x y 8, rewrite them as 2x 4 y and 8 y x Substitute the
first expression into the second: 8 2(2x 4)
x and solve for x; this yields 12 3x or 4 x.
24 a Substituting x 3 and y 2 into the equa-tion 5x2 2xy3we get: 5(3)2 2(3)(2)3 (5)(9)
(2)(3)(8) 45 (6)(8) 45 (48)
3
25 c When you substitute a 2, b 1, and c
12, into the expression
2ac b 5 you get:
which simplifies to:
which equals:
10 divided by 12is the same thing as 10 times 2, which equals 20
10
12
4 1 5
12
2(2) (1) 5
12
– BASIC SKILLS FOR COLLEGE –
Trang 3C • 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
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102
P RACTICE G RAMMAR T EST
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 –
Trang 57 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.
_ _
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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 –