Download 3. -x+2--x-6 5 10 =~x !-x+ 2- 6 Groupliketerms 5 10 6 1 4 W .fr 5 =-x

-- Section 3.2
1. Distributive Property
5(x+
3)
3
= 5*x+
5*3
= 5x+
15
1
3. -x+2--x-6
5
10
=~x
5
6
!-x+ 2- 6 Groupliketerms
10
'
'
.
1
4 Wnte fractlOnsW1th
=-x--x10
10
common denominators
5
=-x-4
10
1
=-x-4
2
Combine like terms
Simplify the fraction
-
44
Chapter 3: Linear Equations
5.
6(x
=
+
6*x
=6x
5)
+
+ 2x
-7
+ 2x
6*5
+ 30 + 2x
-
=6x + 2x + 30 -7
= 8x+ 23
5
-(x-6)+x-4
3
5
5
=-*x--*6+x-4
3
3
e.
-7
Use
7
property
Simplify
Group like terms
the distributive
property
Simplify
-
7. a. e2+ 3e - 2e2 + 8e 5
= 1e2 - 2e2 + 3e + 8e
= - 1e2 + lie - 5
-5
Use the distributive
Group like terms
Combine like
terms
5
=-x-10+x-4
3
Simplify
=x+
Use the rule for
-1O+x+-4
3
subtraction
=x+x+
b. -(x+ 2) - 3x + 7
=-l(x + 2) - 3x + 7
3
Use the special
property of -1, b
Use the distributive
= -lx+ -2-3x+ 7
5
3
-10+ -4
=-x+-x+
3 3
= -lx+ -3x+ -2+ 7
=-4x+ 5
Combinelike terms
=x+ -14
3
8
=-x-14
3
Use the rule for
subtraction
c. 2 inches2+ 5 inches + 7 inches2
= 2 inches2
+ 7 inches2 + 5 inches
= 9 inches2
+ 5 inches
Group like terms
9.
a.
2-3x+
15 =4+
x-6
-3x + 17 = x - 2 Combine liketerms
Combine like terms
d. 2(3x
-
7)
= 2*3x
-
+ -l(x - 4) + 5
2*7
+ -l*x
Add -x on both sides
Use the special
property of" 1, c
- -1*4 + 5
distributive
=6x-14+-lx+4+5
=6x+
-14+ -lx+4 + 5
=6x+-1x+-14+4+5
= 5x + -5
=5x-5
on
both sides
- (x - 4) + 5
=2(3x - 7)
Write fractions
with
common denominator
property
Use the rule for
subtraction
Group like terms
Combine like terms
= -Ix + -2 + -3x + 7
Group like terms
-10+-4
Combine like terms
-4x+17= -2
+-17 Add -17 on both sides
+-17
Use the
property
-4x=-19
Simplify
Use the rule for
subtraction
Group like terms
Combine like
terms
Use the rule for
subtraction
- 4x
---4
Combine constant ternis
-19
Multiply both .sides by -.!.
4
-4
19
x=4
Simplify on both sides
=4.75
b.
7 = 4x -3 -7x-11
7 = -3x - 14 Add like terms on right side
+14 + 14
Add 14on both sides
Combine constant terms
21 -3x
--Multiply both sides by -.!.
3
-3 -3
-7 = x orx = -7 Simplifyon bothsides
@ Houghton Mifflin Company. All rights reserved.
Section 3.2
=2.6
-.5x + 2 = 2.6
11.
c. .6x+2 -1.lx
Total Dlsance Traveled
.
'
Mul tlpIy b 0th Sld es
.6
-.5
-.5
-1
by .5
1
1
-(2x+5)~x=-(5x-2)
4
2
1
1
1
1
-* 2x+-*5 -x=-*5x--*2
Use the
4
4
2
2
distributive property
'
.
1
5
5
1 SImpl 1fy
-x+--x=-x2
4
2
1
255
.
-x - -x + - = -x -1 Group like tenns
2
2
4 2
.
- 1
5 5
-x+-=-x-.
1 Combme lik e
Fastercar
Slowercar
travels
travels 55t mUes
40t m!1es
a. Distance = rate * time
The fIrst car travels 40 miles per hour for t
hours, giving a distance of 40t miles.
The second car travels 55 miles per hour for t
hours, giving a distance of 55t miles.
x = -1.2 Simplify on both sides
d.
Is 57 MIles
Combine like tenns
+-2 +-2 Add -2 on bothsides
-.5x =.6 Combine constant tenns
- .5x
-=-
45
b. 40t + 55t = 57
c. 40t + 55t = 57
95t = 57
Combine like tenns on left side
95t
95
= 57
95
t=
Multiply by 1/95 on both sides
t t
; in
hour or 36 minutes, the two
cars are 57 miles apart.
13. a. x + 10 represents the measure of angle B and
2x represents angle C
B
Angle
x+ 10
242
tenns
c
-5
Add -x on
2
b. The sum of the angles is 180°.
x + x + 10 + 2x = 180
both sides
_
5 _
3 x+-= 1
C. x+ x+ 10+ 2x =180
4x+l0=180
170
x=-=42.5
4
The measure of angle A is 42.5°.
Combine like
4
tenns
-5
Add - on
4
both sides
15. Let x represent the measure of angle A, then
2x + 5 represents angle B, and x
Combine
constant tenns
- 5 -4 - 5 - 9
( -1 + 4" = 4"+ 4" = 4")
-1
-1-9
- * -3x = - *
334
-
Multiply by
--1 on both sides
3
3
x=-=.75
4
-
15 represents
angle C.
x+ 2x+ 5 + x-15 =180
4x-l0=180
4x = 190
190
x=-=47.5
4
The measure of angle A is 47.5°,
angleB is 2*47.5 + 5 = 100°, and
angle Cis 47.5 - 15 = 32.5°.
Skills and Review 3.2
Simplify on
both sides
17.
2x - 5 = "lOx + 7
Original equation
?
2*1- 5
"10*1+ 7 Substitute 1 for x
2-5
=
= "10+7
-3 =-3
@ Houghton Mifflin Company. All rights reserved.
Simplify on both sides
The solution x = 1 checks
46
- --
Chapter 3: Linear Equations
1
-
8
5x+24
- -
19. If we can show that 3 x + 5 equals
15
the two expressions are equivalent.
1
8 ? 5x + 24
-x +_=_
3 5 15
25.
, then
-16 feet
"
"
"
_+_=-
_ =_
nte-xas-
Yes the expressions are equivalent because we
1
8 5x + 24
were able to show that 3 x + -5 = 15 "
-
21.
-
5
C =-(F -32) whenF = 14°
9
C= ~(l4-32)
9
Substitute14forF
C = ~Cl8)
9
Simplifyonrightside
C = -10
The Celsius temperature is -10° when the
Fahrenheit temperature is 14°"
23. -8 + cll9 + 6 Horizontal fraction bar is a
9-10
symbolof grouping, perform
operations innumerator and
denomintor before dividing
= -8+~
9-10
Take the 19 power of -1
= -8+2--1
Add -1 and 6 in numerator,
subtract 10 from 9 in denominator
=-8+-5
Divide 5 by -1
= -13
Calculator keystrokes: -8 + (("1)"19 + 6)/(9 -10)
2
seconds) + 150 feet
SOfeet
seconds) + -(2
seconds)+ 150feet
second
Evaluate exponents
"'
= - 64 feet *seconds2 + 100 feet *second + 150 ~d
second2
15
with common denominator
5x
5x 24? 5x + 24 W " 5
15 15
15
15
15
"
"
5x + 24 5x + 24 C omb "me fractlons WIth
15
15
common denominators on left side
SOfeet
2
,:-(2 seconds) + -(2
second
=--;-(4
second
24 ? 5x + 24 W " fra
1 ft d
-x+-=nte ctlOnson e SI e
15
second
ComparetheexpresslOns
5
15
-16 feet
second
Multiply
=
-64feet*~
~
_
~nd'
= -64 feet
= 186
feet
+
100feet*~
_~
+150 feet
~nd
Cancelunitsin fractions
+ 100 feet + 150 feet