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FOR STUDENTS ENTERING: ALGEBRA I/FUNDAMENTALS OF ALG.
I
&¡&ry&#ç$eßr&$eN{
June 20]ó
SMCMS Porents ond Students;
Altoched you willfind o pockef of molh problems lhot should be
completed during the summer monlhs. WE ARE ASKING THE
STUDENTS TO COMPLETE THE EVEN PROBLEMS IN THIS PACKET. AII Of
the problems ore mcth concepls thot were covered during lhe
201 5-l ó school yeor in yourlyour child's mof h closs. The purpose of
this summer ossignment is io help you refoin the informotion lhol wos
leorned over the post 9 months. All moth closses ore siepping stones
for fhe nexl closs so it is importcnt lhol knowledge is retoined from
yeor lo yeor.
The pocket should be completed prior lo the stort of ihe 2016-17
schoolyeor. The pocket informolion moy be token for o grode in
the next school yeor. ln order to help students, moth teochers from
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students with ony difficulty they encounler. The schedule of dotes
ond times will be ovoiloble on www.eccss.orq lofer in June.
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sotisfy fhe summer moth pocket requiremenl.
DATE
NAME
1 lntroduction to Algebra
1-1 Variables
Ob¡ect¡ve:
To simplify numer¡cal expressions and evaluate variable expressions.
Vocabulary
.
Variable A symbol, such as the letter;,
Value of a variable A number that
used to represent one or more numbers.
a variable may represent.
Variable expression An expression, such as x + 5, that contains
Numerical expression, or numeral An expression, such as 6
particuÌar number, called the value of the expression.
òi-ptifyiog un
"*p.ession
*
a variable.
5, that names
a
Replacing a numerical expression by the simpiest
name of its value.
Evaluating an expression Replacing each variable by a given
simplifing the rcsult.
Symbols
CAUTION To
=
(is equal
to)
evaluate ¿å when
multipli.ca¡ion
+
a
:
(is not equal
4 and b
sYmbol: ab : 4'
:
to)
va.lue and
ab or
a'å
(muttipþ)
5, be sure to write a
5.
1. Simplify: a. 4 + (10 - 3) b. (20 + 4) + (6 ;- 3)
Sotution Simplif tþe nunerical expression(s) within parentheses fi¡st.
a.4*(10-3) b.(20+4)+(6+3)
,5 + 2,
4+ 7
Example
11
-'_v-
7
Simpliry each €xpress¡on.
2.8+(30+Z)
1.5+(15-3)
4. 13-(4x2)
7.Q2-L7)x6
10. (8 x 11) - (3 x 1r)
Example 2
8.(36+9)+16
ll. (24 + 6) + (30 + 2)
Evaluate each expression
a,.
Sotution
5.(9+6)+4
Replace x
9.(18+3)+(10+5)
12.(42+?¡+1rxr¡
ifx :2andy =3.
b.
ry
16-(0x7)
6.9+(6+4)
3.
5ry
c.
(6x)
-
3
with 2. Replace y with 3. Insert the multiplication symbol(s).
a.ïy:2.3:6
b.5xy=5.2.3=30
c. (iír)
- 3=.6."7-3
= .t2:3.
=9
DATE
NAME
1-1
Variables þontinued)
if
Evaluate'each expression
3
=
:
J
3r
5, ande
=
0.
yz
l8.3xz
xl
17. 6yz
2t. (u) - 6
14.
13,
Example
¡
22. (52) +
4
Evaluate each expression
a.
- Qy)
(5x)
Solution n.
b.
15. xz
16.4ty
19.2q
20.7x2
23. Qù
-
24. (4x)
3
I
+
(ay)
ifx =6,y:7,and,z=4.
6.(r + z)
*4
-'(v-¡)
".
(lr)
(2y\
\
g:q
\
gJ
Replacex with 6 and y with 7 and
insert the multiplication symbols-
30
14
Simpli$ the expressions within pàrentheses.
I6
+
Subtract.
b.6.(x + z)
il
6.{6 +
6,
Replace -r with 6 and z with 4.
4)
Simplify the expressioir rvithin parentheses.
10
Multiply.
60
c.
b+z) _7+4
(y-x) 7-6
Replace -r with 6, y with 7, and e with 4.
11
Simplif
the numeraior and denominator.
1
Divide.
Evaluate each expression
- (3x)
29. 5 . (x - i)
2s. (2y)
if¡
= 3, ) = 5, and z =
(sx)
30. 4. (x + y)
2;6. (3y)
+
0,
- (62)
31.
-^' *-Ð)
(y - x)
27. (sy)
28. (7ò
12.
\\ + ')
A+z)
Mixed Review Exercises
Perform the indicated operâtions.
l.
4.2
5.
106.4
x
1.3
2.
+
6. 6.72
7.8
16.35
+
-
16.07
3.9
å
o
'' 4 *l-10
n.f;xfr
ß.åx+
M.+x+
2
3. 2.4 + 0.6
7.
50.26
x
1.2
4. 7.3 - 5.6
8. 64 +
11.++-}
12.
j.-
16.
".
+
O.2
9 _3
168
63
714
ÐATE
NAME
1-2 Grouping Symåols
Ob¡ectivè:
To simpl¡fy expressions with and without group¡ng symbols.
Vocabulary,fsymbols
Grouping symbot A symbol used to enclose an expression that should be
simplified first. Multiplication symbols are often left out of expressions
with grouping symbols. For example:
Parentheses
6(s - 3) : 6'2
Fraction Bar
Brackets
6Ís
-
37
=
10+6
9-5
6'2
i6
4
CAUTION When there are no grouping symbols, simpliff in the following order:
1. Do all multiplications and divisions in order ftom left to right.
.
2. Do all additions and subaactions
Example
Simplify:
1
- 2)
8(5)
a. SQ
Solution
ã, 8Q
- 2)
in order from left to right.
b. 8Q) -
2
The parentheses tell you to simplifu
8(5) means
7
-
2 first.
8'5.
40
b. 8(7) 56 -
2
2
Do the multiplic¿tion
8.7
first.
Then subtract 2.
54
Simpüfy each expression.
2. a.
- 3)
b. 12(5) - 3
5.a.9-6+3
b.(9-6)+3
- 1)
b. 9(6) -
1. a. 9(6
1
* 5:2
b.(8+5).2
4. a, 8
a' 15+3
g,-3
Example 2
Simpli$:
Sorution
18
a' 15+3
s-3 =7
12(5
3. a. 6 * 4.5
b. (6 +4).s
6- a. lZ+8+4
b.(12+8)+4
,b' 8-5 +2
2(B -Ð
Simplify the numerator and denomhator first.
Then divide by 6.
- 8.5+2 40+2
"' z(a - s) - 2(3)
42
6
Start to simpliry tl¡e numerator and denominator,
Further simplifu the numerator and denominator
Then divide by 6.
3
NAME
1*2
ÐATË
Grouping
Sfnbols
(continued)
Simplify each expression.
n" 6+9
7-:2
".#+ n.y#
Example
3
ts.6'-3,-+211
M-L+
2(9-Ð
3(5 -
Bvaluate each expression
if a = 6,b
a.a(b+4 b.ry
aSolutíon
t.
a(b
*
c)
: 6(2 + 3)
: 6(5)
: 30
, 8(c+ð
a-h
o.5-4
to.ffi
e.t
a l1 -3
"'2+6
3)
:2,c:3,ardd:O.
h
Replace a with 6, å with 2, and c with 3.
Simplify the expression within perentheses
Mulriply.
8ß +01
Replace the variables with their given values.
6-Z
: -c(Ð
Simplify the numerâtor and denominator.
4
24
Divide.
.4
:Ã
¡ = 2, ! : 4, z = 6, and ó = 5.
16.a.5y- 1
17. a. 16-3b
Evaluate each expression if
15. à.2ic + 5
, b. 2(x + 5)
1\a.bx*y
y)
23, 5(4y - 3x)
b. å(x +
27.
ry
x+z
- Ð
20.a.n-b
b. x(z - b)
A. 6z - zxy
b. 5(I
2s.
b.
(16
.-
18. a. 3z + 4.
b. 3(z + 4)
3Jb
2!. a.2ry +z
b. 2(xy +
h.
-5
2s- :,,¿ - z,
25. ryz
-Er-.r
z-b
5(b
-
-b
- b)
22, a. 6ryz
z)
yl
6x(yz
26.
x(y.y +
30.
?ry)
x+y
Mixed Review Exercises
Simplify.
3
4.9+ 15 +3
.1. (12
-
Evaluate eaeh expressiori if
7.
5ab
l0.o+"
c-at
2.20'8 + 18.2
S. lzs +3) + (8 +2)
6) +
a=
2, b
8.
1r.
=
3, and ¿
=
6. (7 + sr.(8
4.
9. (2c)
bc
(7a)
3.sxQ5-7)
-
(4b)
12. 6a
-
3
-
2)
z)
DATE
NAMË
2-3
Rules for AddÍtion
Ob¡ective:
To add real numbers using rules for add¡t¡on.
Vocabulary
sþs
Opposite
A positive and
a negative number are said 1o have opposite signs.
Examples
Rules for Addition
2+5
If
two numbers have lhe same sign,
add their absolute values and put
their common sign befo¡e the result.
=7
-2+(-s)=-7
If
two numbers have opposite signs,
subtract the lesser absolute value
6+(-4):6-4:2
(-6)+4=-(6-4)=*2
from the greater and put the sigIt
of the number having the greâter
absolute value before the result.
If
two numbers are opposites,
then their sum is zero.
3+(-3)=0
+(-9).
Exañple
1
Add6 + (-8)
Sotution
'1
Add the numbers in order fr'om left to right.
+
13
5+(-8).+13+(-9)
.-2
+ 13.+ (-9)
+ (-9),
.il
-.--=----..\/-
!-..-ìJ+
2
Solution 2
l.
Add positilr
numbers. 2.
6-8
13
Add negative numbers.
3.
Add the results
t9
19
-g
-17
-17
'2
Ädd.
1.
6
2
-4
-7
2.
8.
-35
-s6
120
3. -7
4. -3
5-
6
9.
126
10. -
14s
11.
23
6.
-56
64
J1
136
12. -162
323
-35
309
_11
-58
-r7
.-82
-¿5
.47
-82
Add.
13.(-8+5)+2
L6.
(-2 + 6) + (-4)
14. (-12
+ 15) + 6
*5
+ (-3) + s
17.
ts. (-4 + 8) + (-3)
18. -4 + (-14) + 4
23
DATE
NAME
'2,-3
Rules for AdditiÒn þontinùed)
Add.
-6 + (-U) + 6
22. (-3 + 3) + 17 + (-'7)
24. -7 + (-s) + (-6)
26. -7s + 10 + (-3).+ (-2)
16+5+(-8)
21. ( 3+3)+7 +(-r1)
20.
19.
23.
-2 + (-4) + (-8)
2s.-3+(-9)+7+(-5)
+ (-5) + (-x) +7.
Example 2
Simplify 3
So¡ut¡on
3 + (-s) + (--x) + 7
:
:
-x
_,
*êjJ+ (-s)
+ lg__ltg
:*x+
RegÌollp Ρe lerms
Simpli&.
5
Simplify.
28.3+(-8)+(-y)+(-i1)
30. -5 +2a*8+7
27.-2+r+(-6)+3
29.-5+2n+3+(-3)
3I. 17+8å+( 15) + (-10)
33.
32.
-(-7) + 3), + (-6) + 4
-Í6 + (-1)l + (-c) + 2
34. 3x +. V
Example 3
EvaiuateÌ + y
+ (-2) if x = -2,andy
Solution
l
:
:
+ }' + (-2)
5.+ (-2)
"+ +
.3
\.-.--------v- t?,
(-2)
:
Eraluate each expression if
35.y+z+ (-2)
37. -11. + ( -:r)
39. 1+(-])+r
+ (-y)
1
:
+ (-2) + (-3)l
5.
Substitute
-2 forr
and 5 for y.
Add from left to right.
Shirplify.
¡= -2,y = 5, andz = -3.
36. -18+r+)
-z + (-7) + y
40. -x + (-y) + (-15).
38.
Mixed Review Exercises
Simplify.
2.7.5'3.2
1.3+8{-2
4. l-el
-
7
-t' 9,6+9.4
6* z
10. Uz +
24
(-2)l +
5
s. l-1.61 + r.6
3. (9 - 6 + 3)'2
6. l-111 l-sl
s.:|+|+$
9.2.7+1.0+3.3
11.
(-7 + 2) + (-3)
-
12.-2+(-8)+7+(-1)
DATE
NAME
2-4
Subtracting Reat Numbers
express¡ons involving differences'
To subtract real numbers and to simplity
Obiective:
Definition of Subtract¡ón
opposiæ of b'
To subtract a real number b, add the
ã-b=a+(-b)
ForexamPle,3 - 9 = 3 + (-9) = -6'
b'-6-3
SimplifY: a'2-7
Examqle 1
1
-
(-
8)
a.2-7:2+(-7)=-5
b. -6- 3¿ -6+ (-3) = -9
c.-2-(-8):-2+8:6
Sorufion
cAuTloN
c. -2
Subtractio¡ is n¿, coÍ)rnutative '
7 -3:4'
btt3-7=-4,
so7-3+3-7
CAUTION 2
Subtraction is zof âssociative'
0 -3') -2:4-2=2'
- (3 - 2\ :7 - 1 = 6'
so(7 - 3) -2+7 -(3 -2)
uutì
SimplifY'
?2. -15
24.
26. s6
-
5.0-5
8.-8-1
11. -8 - (-3)
t4.36 - (-34)
(4s
23. -8
25.
n.
32)
-
(-24)
(-15)
- 3.5
zr. 2.65 - (-2.35)
28.214-(54-66)
30. (25 - 32)
32, (z - 7) -
-3 -
-
!9. -2.3
-2
-
ts. -2s
17.
decreased bY 5
18 lebs than
3.9-13
6. 0 - (-3)
9.3 - (-3)
t2. 36 - 216
2. 17 -11
-9
4.6-16
7. -12-0
x0. 7 - (-5)
L3. 7ß - no
16. -ls - (-3)
18. -17 - (-8)
29. -4.2 - 5-6
1,25
(44
-
Grz +
s5)
15)
-
decreased bY
10 less than
29. J.67 31. (46 33. (32 L25
-i4
-6
- 35)
QO - 4s)
so) - (6s - 40)
24) - (-6 + 9)
(160
25
NAME
DATE
2-4 Subtracting Rèal Numbers
Gantjnugd)
"
Example 2
Simpli{13-9-8+5.'
Solutlon
13-9-8+5=13-9-8+5
=i3+(-9)+(_8)+5
+ (-8)+5
.4
\-,,
-*
-
=
*ì
1
Sürplify.
34.3-4+7-15+21
36.-5-18+6_7+10
14- 12+ 11 +3 _20
37. -9 -.21 +3 -8 +30
35.
Êxample 3
Simpli$: a. -(x - 5) b. _(3 _ y) c. _(_2 + a)
Solution
To find the opposite of a sum or a difference, you
change the sign of each term
the sum or difference.
ã-
-(n-5)= -¡+5
b. _(3
of
_y): _3+y
c. -(-2*a):2-o
Simplify.
38. -(x + 2)
42. -(y - s)
39. -(4
43. -(8
- y)
- r)
Example 4
SimplifS-(,x+3).
Solut¡on
8
-
+ 3) = 8 -*
(.r
-(-7 + a)
44. -(b - 6)
40.
-
3
=(8_3)_f
=5 -¡
41.
-(x
45.
-Q + n)
Change the sign of each term of.x
Regroup the terms.
*
-
3)
3
Simplig,.
Simplify.
46.6-(J+4)
47.4-(q_6)
Mixed Review Exercises
1. l-61 + l2l
,
l-åi- l-+i
7. ls + (-9)1 + 7
10. -2.4 + s.3 + (-3.6)
26
48,x-(x+2)
2.r7.2.3.s
3.2*6x+5y*8
. (-+)
'. -+*
8. 3.4
11,.
0.5 + (_i.4)
-27 + (-28) +
49.n-(_3+n)
18
+
47
o. 11
4 + /-aa\
\ -4/
9. *4 + [-6 + (-2)]
12. 2 + (-3) + (-10) + (-x)
DATE
NAME
2-6
Rules for Multiplication
Ob¡ective:
To multiply real numbers.
Examples
Pmperties
Identity Property of Mültiplication
The product of a number and
to the number itself,
a,1
=
a
I
is identical
and l'a:
the product itself is zero.
6.0=0
and
0.6:0
and
(-1)6: -6
-6
6(-1) =
(*5X-1):-(-5)=s
For every ¡eal number a:
-a
1.6:6
and 0'¿:0
Multiplication Property of -:1
a(-l):
and
a
Multiplication hoperty of Zem
When one of the factors of a pìoduct is zero,
a.0=O
6.1:6
and (- i)(-s)
and (- l)a = -a
Property of Opposites in Products
' For all real numbers ¿ and å:
(-4X5)
: -(-s) :
:
s
-20
4(-s) : .20
(-4)(-5) :20
(-a)(b) : -ab
a(-b) : -o5
(-a)(-b) : ab
Rules for Multiplicat¡on
1. If two numbers h^\e
If
sign, lheir product ispositive.
two numbers have opposite signs, their product is negative.
r}re same
2. The product of a¡ svez number of negative numbers is positive.
The product of an odd ntnúer of rrcgative numbers is negative.
Example
1
SaJution
Multiply: a. 3(6)
a.3(6):18
b. (-3)(6) : -16
c. 3(-6) : -18
d. (-3x-6) : 18
Examptre 2
b.
(-3X6)
c.
3(-6)
@oth factors have the same
d. (-3)(-6)
sþ.)
(The two factors have opposite signs.).
(The two factors have opposite signs-)
(Both factors have the same sign.)
a. 2(-3)(-4)(-5) is negative because it has 3 negative factors.
b. (- lX-4X -5)(6X -7) is positive because it has 4 negative factors.
c. (-6X7X0X-4) is zero because it has a zero facfor.
to
NAME
'2-6
DATE
Rules íor Multiplication þont¡nued)
Multipty.
1. (-12X-3)
2. 18(-4)
6. (4X-7)(10)
s. (-2)(sx-8)
9. 35(-26X0)
10.
s(-2x-8x-s)
4. 18(0)
8. (-1rX-12X0)
3. 2(t"t)
7. (-2)(-3)(-4)
11. (-7X3X-1X2)
Exainple 3
Simpli$: a, (-2.x)(-6y)
b. 3y + (-7y)
So/utio',
a. (-2x)(-6y)
:
:
:
b. 3y + (-7¡,)
(-2)x(-6)y
(_2)(_6)xy
lbcy
12.
:
:
:
(-8X-5X-lX-3)
t3 + (-T)ly
(-4)y
*4y
Simplify.
13.
(-3a)(-4b)
L4. (sx)(6y)
18.
-7a 'r (-8ø)
19. 2x
+ (-5x)
ts. 2p(-5q)
20, 8x + (-3x)
4 Simpliff: . t. -3Qx - y)
Sotuf¡on a. -3(7x - )) : -9@Ð -. (-3)(y)
t6. (-4e)(7Í)
27. (-Ily) +
17. (-6a)(-sb)
3y
22. -4n
i
4n
b.5x-4(r-1)
Example
b. 5x -
_6x _ (_3y)
=
__6x+3y
4(x
- (4x -.4.
=5x-(4x-4)
=5x-4x14
=x*4
¡- 1) 1
5-r.
Simplify.
23. 6(x * 2y)
?-6. -l(ay - 5)
?9. 4x - 3(x - Z)
32.(-1)(a-b+2)
35.4x-2,x*74x
24. -SQc + d)
27. (3x - s)(-6)
30. 6r - 2(x + 3)
33.(-1X2r-)-3)
36.2y-5-5y+3
25. -4Qm + 2n)
2.8. (-3 + 5y)(-2)
31. 3x - 5(¡ - 1)
34.(-L)(x+y-2.)
37. 1lp
-6c -7c +9p
Mixed Review Exercises
ïlanslate
each seutence into an equation.
1.
Three times a number is 27.
2.
The quotient of z and 4 is 15.
3.
One half of a number is nine.
4.
Six less than twice a number is 14.
Simplify.
5. 1r0
-
8. 3(20 +
30
(12
5)
-
8)
6. 161 - (8 9. 2n + (-5n)
11)
7. 2.+ (*s) +
10,5(n+1)+7
(-y) +
9
1)
NAME
DATE
:,.;i 3 Solving Equations and Problems
3-1 Transtorming
Obiective:
Eqwations: Additiøn and Subtraction
To solve equat¡ons using add¡tion and subtraction.
Properties
Addition Property of Equality If the
same number is added to equal
numbers, the sums are equal.
Subtraction Property of Equality If the same number is subtracted from
equal numbers, the differences are equal.
Vocabulary
Equivalent equatioru Equations that have tle same solution set over a given domain.
Transformations Operâtions on an equation that produce a simpler equivalent equation.
By substitution You can substitute an equivalent expression for any
expression il an equation. You do this when you simpliff an
expression in an equatiou.
By addition You can add the same number to each side of an equation.
Ey subtrâction You car suútract the same number from each side of an equation.
cAUTloN
Example
Tb check your work, you should check that each solution of
the final equation satisfies the onþzal equation.
1
Solution
Solve¡-6:11.
x-6:!1
x-616:11.+6
x:L7
Check: x
77 -
6:
,|
6 ,:.
11
11+11
:11 V
To get x alone on one side,
add 6 to each side and then simpli$r.
O¡iginal equation.
Substitute 17
for*.
The solution set is {17}.
Solve.
1.a-9=11
4.d-14=5
7. x - 6 :27
2.b-5:13
5.¡-15=0
Lq-7=11
3.x-20=-19
6.v-27:-54
9.q-9:-16
37
DATE
NAME
Tänsfôlf'ning Equations: Addltlon and SubtrcetiÐn'
3-1
Exanple 2
Solve-9:n*11
Sorution
'9=n*11
-9-11 :z*1I -20 =
Check:
n
[To get n alone on one side,
lsubtract 11 from each side.
Simplifu.
11
-9 = n * lI.-
-s :2
-9
-zo +
-9 \i
(continaed)'
Original equation
1l
subsritute -2o
for n.
The soiution set is { -20}
Solve.
10.
-6:m+6
ll.2l:x+15
p+
15:d+60=-15
= -22'
18. 35 -;r + 16
14.
18
79.
23.
22.x+1.5:6.8
Example
3
Solution
Solve
-4:u-6
-26+m:24
16. 14+r=0
2¡.22=y+3
-1 +a=0.5
24.3.9=y-r.4
-x -l 5 :
4.
-x*5:4
-¡ 5 - 5.:.4 1-
Check:
n: 63
- 72
21.¿-8:-10
25. 7.5 : w - 2.5
13. -37 +
1'7. 29 = y
12.
5
.
-x+ 5 =4 .--1 +5!4
4 = 4.,1
JTo get -r alone on one side,
Isr.rbl¡act 5.from.each side anct simplify.
ilf the opposite of a number is -1,
Ithe number must be l -
O¡iginal equation
Subsritute I for ï.
The solution set is {1}
Solve.
-x+3=5
29.7 -y:11
32.-5-y=7
x: 18
31. 13 =22-y
-y+7:17
30.9:-x+16
33. 10= -12-e
28. 12 -
27.
26.
34.t5=_y+10
Mixed Review Exercises
Eraluateif¿ = 3, b
t. a-lb- cl
, a-2b
4.-.'.a+d
= -6, c = -4,
and.d
=
2.
z. (lcl - d)
- 3bIc-d
-
(ltl
-
o)
tt.
tul
38
*
(-å)
zab
c+d
-
Simplify.
7. (-3X-4X8)
3.3lcl
8. (-7 - 1.6) + (-7
.24\
9. 252
:
(-36)
DATE
NAME
3-2
Transforming Equations: Multiplìcation anp Division
Ob¡ective:
To solve equations using multipl¡cation or d¡vis¡on.
Properties
'
Multiplication Property of Equality If equal numbers are multiplied by the
.
same number, the products are equal.
Division Property of Equality If equal numbers are divided by the
same
nonzero rnmber, the quotients are equal.
Transformations
By multiplication You can multþ1y each side of an equationby lhe
By division You can divide each side of an equation by
CAUTION
I
same nonzera real number
The s?lrîe non¿ero
real number.
When you transform an equation, never multiply or divide
bY zero.
CAUTION
2
Example
lVhen you multiply or divide by a negative number, be
careful with the sign of your answer.
1
Solve
Solution
:
4x
4r
128.
128
[To get x atone on one side, divìde each side
lby 4 (or multiply by , the reciprocal of 4)
44
x:32
Check: 4x:
a}z¡
f
128
!
ns
128 :
128
The solution set is {32}
"l
Solve.
:
l.
7m
4.
7.
= -r43
108 = -9x
2. l2n
140
*rlf
:
3. -8.x =
240
5. -720 : -245
8. 45k : -270
t2
96
6. 330
: -l5u
9. 26n
=
-570
: -in.
Example 2
Solve
Solufion
-*ozt: -+(-+,)
-16:n
Check: 12
12
get n alone on one side, multiply each
[To
\43
by
Iside
-5,
the reciprocal
of
-;.
: -]n
=')7 -iG16)
. rz
-
1õ
tL\l I
Ttre solution set is
{-16}
39
NAME
3-2
DATE
T
ransloltnr' ing' Eguatl õns : M
ultiiilicatícn end Ðívisiori
Solve.
n.lm=s
n.
-!t
16.
¡r
=
-zo
3
Sorufion
4v
u.
?d = -40
n. -|x = +o
s. |e = -24
-Is
n. -l6e = Mo
= -s6
Example
:
11.
Solve: a.
ß.
-ln = -zt
^i
rt
I
b.
1:-o
(contirtuêd)
în
I
2\t) = 2(-6)
' x: -12
^/
1
\
,(+)
'\1)"
n
T,
Lheck: ¿ = -o
*z-u
7
t"i
Check:
1
-6: -6J
The solution set is
7
2
2n
2
?1
-2
')
(7)
7
2
{-12}
7
2
7
2
The solution set is {7}
Solve.
i : -24
22. -t = t5
Le.
zs.
Ir)" = z!J
20.
+ = -zs
zt.
-# : t2
23.
-28: +
z+.
-tx = zt
ze.
!ø = zrJ-
zt. -Iy
J'
=
tZJ
Mixed Review Exercises
Evaluateif¿: -2,b = 3,andc: -6;
l. 6b - ?a
2. Qb - 5c)a
a. lbl - la + cl..
s. -0:b\
c
3.
lcl+lal-b
- 8+a
ô.c
Simplift.
7.6a*5I7a
I0. -3(m + 4)
40
8.7n-6+6
11. (r + 5)6
9,9p-p+3
12.2(3y
-
4)