-ffi
Solve.
u
I
(x + 4)(x
-
2)
:0
or x-2:0
x*4:0
x:-4 ot
i
ri
Using the principle of zero products
5olving each equation seParatelY
x:2
@+0@-2)-0
Check:
1z++112-2)10
CZI+I(-4-2)lo
6.010
Therearetwosolutions,-4andZ'Wecanshowthesolutionsasasetby
U;rg them
i-4'
inside braces'The solution set is
2)'
Solve.
:0
7x:0 or 4x * 2:0
7x(4x + 2)
4x:-2
* : _1.
x:0 or
x : 0 or
The solutions are
Using the principle of zero products
Solving each equation separately
and -).The solution set is
0
{o'
-}}'
Solve.
(-2x+s)(sx+1) -Q
5x+1:0
-2x+5:O or
5x: -L
or
-2x: -5
x:) <1 or
x:-5
rs
_L\
The solution set ts {}, -s-}.
Try
This
d. (x
-
Extra HelP
On the Web
Look for worked-out
examples at the Prentice
HallWeb site'
www.Phschool.com
Solve.
19)(x + 5)
: o
e' x(3x
-
1-7)
:
s
f.
(9x + 2)(-6x + 3)
:
0
X*€ ffixmrymEses
A
Solve.
t 1*?n:1:
4. 0.9Y - 0.7 4.2
7.2(x + 6):8x
10. 27 :9(5y
-
l*fr":t
:
5.
-
3.
z.
2)
0.8,
0.3t
6.5
s.3(y+5):BY
LL. 180(n - 2):900
-Z*
6. 1.4x
9.
12.
80:
*L=
-ru
+ 5.02:
10(3r
O.4x
+ 2)
210(x-3)=840
l1
il
:l
:1
:;l
ta
64
Chapter
2
Equations and Inequalities
t"
).1
:;.i
;."1
'1"
14, 8x - (3x - 5) : 40
t6. 0.9(2x + 8) : 20 - (x + 5)
13. 5Y - (2Y 15. 0.7(3x + 6)
l0):25
: 1..1. - (x + 2)
n.f$@
- 17: -i$y - L6) n.[{rzt + 48) - 20:-t?4t -
+ 8)
t44)
19. a * (a - 3) : (a * 2) - (a + 1) 20. 0.8 - 4(b - 1) : 0.2 + 3(4 - b)
22. (x+ 4@- 8) =0
2L. (x+z)(x -5):0
(t-3)(t-7):0
2s. (2x-3)(3x-2):0
23.(y -8)(y-e):0 24.
28. (3y - D$y- 1):0
27. m(m-8):0
26. p(p-5): 0
B
Solve.
29. x(x
-
1Xx
+2):0
t. l@-3)(7a+4):o
:
33. 0.5(x - 2)
Solve for x.
-
2(x
-
s)
30.
y(y-00+2):0
32.z+(i-1)
s)
0.4(x- - s(x - 2)
: x-24
lS. 1.6x_4:f
36.cx*3h:5a
34.9x+3:c
39. 5x * ax:19
37. 7x - 3: ax * 5b 38. ax - bx:72
:
40. Contrast solving 0.8y - 1.2 -7.6y by first clearing decimals with
solving without first clearing decimals. Which would you do using a
calculator? Why?
41.
Critical Thinking Write
an equation that has both 7 and
-8
as
solutions.
Challenge
Solve.
42.x,x:1,
44. x(x - 1): x
43.x'x:x
45. x(x - 1): x(x+1)
46. What is the solution set for each equation?
a. x(x - 1)(, - 2)(* - 3)'.. : 0
b. (x - 1)(, - 2)(x - 3)... : 0
c. (x * 1)(x + 2)(x + 3)... : 0
d. x(x - 2)(* * 4)(x - 6) "' : 0
e. x(x - 10)(x - 20)(x - 30) "' - 0
f. ... (x + 3)(x + 2)(x + l)x(x- 1)(,
r
- 2)(x- 3)"' :
0
Mixed Reuiew
Simplify. 47. 42 . 43 . x0 a8, ?y)t(-y)' 49. x3 . x-s 50. (3c'z)3 t-7, t-8
Convert to scientific notation. 51. 390,040 52. 0.000421 53. 24.072 1-9
Convert to standard notation. 54, 4.03 x 10-6 55. -8.22 x LO6 Lg
2-1
More on Solving Equations 65
i,
ii
Extra Help
On the Web
i.
t:
l!
Look for worked-out
examples at the Prentice
Hall Web site.
www.phschool.com
A\
Solve.
: lns,for I (an area formula)
W : El,for 1(an electricity formula)
F : ma,for rn (a physics formula)
I : Prt,for r (an interest formula)
E : mc2,for m (arelativity formula)
11. P : 2l + 2us,for / (a perimeter formula)
L.
3.
5.
7,
9.
13.
15.
A
c2:
a2
+
b2,f.or
a2(ageometryformula)
2. A : lu,for u
4. W - El,for E
6. F : ma,for a
8. 1 : Prt,for P
L0. E : mcz,for c2
12. P : 2l + Ztn,for w
14.
16.
c2:
+ bz,forb2
nrz,for fi
a2
A:
A: firz,f.or r2 (an area formula)
17. c =!fo - 3l),forF (a temperature formula) 18. * : *f, - 40),f.or h
20. V : tnr',for n
lg. V : lxrt,for 13 (a volume formula)
21. A:tno + )na.forh(anareaformula) 22. A:)no +lnt.rcro
24. F : (,for r'
f.or m (aphysics formula)
23. F.
B
Solve.
't-
26. A: firs + r2,fors
25. s = u,t * )atz,for a
you
formula
I : Prt for r. Use it to find how
solved the
27. In Exercise 7,
to
earn
deposit
of
long it will take a
$3 when invested at L)o/o simple
$75
interest.
8, you solved the formula I : Prt for P. Use it to find how
much principal would be needed to earn $6 in two thirds of ayear at
12% simple interest.
Zg. Critical Thinking In Exercises L3 and 19 you solved for a2 and 13,
respectively. Tell how you could use a calculator to find a and r.
28. In Exercise
Challenge
30. A gas formula from physict ir + : '+ Solve it for
31. Solve the gas formula of Exercise 30 f.or Tr.
i
ilUEfrxed ffiew[euu
Simplify. 32. (xz)z 33.10:;-z
36. 0.4n + 2.7 : 5.1, st.|+1,
40.4n-(3r+6): -1
72
L
I
Chapter
2
V,.
Equations and Inequalities
:i
34. (2m2n)z
(S-z;-: 1-B
1. 1
,r. 8"
6
35.
t
lm-z:
41. (x
4)(x + 5)=o
r*.
-
I -5, 2-1
1
1.2
Extra Help
On theWeb
E*& ffixercf;ses
A
MentAl
Math
Determine whether the specified number is a solution of
the inequality.
l.
2y
2. 5y -2>3y +
-5 > -10;3
8;8
3- 6 - v
Graph.
4.
Look for worked-out
examples at the Prentice
5. y<-1
x<4
6.
x>5
7.
HallWeb site.
www.phschool.com
<9;-3
x>3
Solve.
1.1.-t+L4>9
10.y+3<9
9.x+5>2
8.r+8>3
15, 0.5x <25
8x>24
12. x -9< 10 13. y -8> -14 14.
s. -lt, = -f,
:16. -ex = -8.1 t7. _'8y < 3.2 18. -?, > -;
22. 5y*2y<-21
21. 5y+13>28
20.2x+7<1.9
25- 8x-9<3x- 11'
23. -9x-t3x> -24 24. 2y -7 <5y - 9
27.0-2y + 1> 2.4y - L0
26. O.4x + 5 < 1..2x - 4
28. Enor Analysis Jadranko says the solution to y - 9 > -18 is
y < -9.What error has he made?
B
Solve.
29.
3L.
33.
*-L=-$+zx
30. 2x
-
3
<
t* * t0 - L.25x
32.4m+5=M(m-2)
aly-2)=9(2Y+5)
Critical Thinking
Find two different inequalities whose solution
sets contain all real numbers less than -5.
Challenge
Solve.
3a.
0+ 3)(y- 3) <0
3s.
y(y+
5)
>0 x. T!tr>o n. fi<o
38. Determine whether the statement is true. If false, give a counterexample.
a. For any real numbers a, b, c, and d, if- a < b and c ( d, then
a-c1b-d.
b. For any real numbers x
and
y,if x < y then
x2-< y2.
"' l$ixed'ffiewEewa
Simplify. 39. a5 '
a-3
' a2
40. (6x3y5)2 41. (2m5)z +Z-
25
+5.
(#)'
18
44. Tlne sum of three consecutive integers is 65 more than twice
the first integer. Find the three integers. 2-2
Z-4
Solving
Inequalities 77