Chapter 3: Linear Equations
Section
245
1.
llx = 20x -18
+-20x +-20x
-9x = -18
7.
3.1
= 60t
+ -95
+95
Add
+ -95
=
150 60t
1
1
-*150=-*60t
60
60
1 150 1 60
-95
on
both
-1
-1
-*-9x=
-*-18
9
9
x=2
Multiplyboth sidesby2-
60
Write
150
and
60
9.
as
Multiply
numerator
numerator
Multiplybothsidesby
3x+20 = 6x+2
times
and
3x+-6x=6x+-18+-6x
denominator times
denominator
5
-=t
2
The
variable
we
may
write
this is t
3.
is usually
= 2.5
shown
the solution
on
as t
the left side, so
= ~.
2
As
a decimal
8=2x-6
Add
14= 2x
1
1
-*14=-*2x
2
2
14 2
6 on both sides
Combine
-=-x
2 2
11.
constant terms
Multiply
both
sides
Multiply
numerator
by
2
.!..
times
7=x
1.8b - 3.4 =
J
+3.4
1.8b
=-6.8
* 1.8b
=J
1.8
* -6.8
b
=-3.7
b=
feature
-34
9
-
to write-3.7as
Divide both
-2-
.
3
Wntex as -x
3
-1
Add - x on bothsides
3
Combine constant terms
Add 3.4 on both sides
Combine constantterms
Multiply
both
sides
by
1.8
b=-6.8
1.8
-18
-3
_
2
16=-x
3
-10.2
+3.4
-3x
-=-3
Combine like terms
-7 =9+~x Combine like terms
3
Add -9 on both sides
+-9 +-9
times denominator
5.
=-18
1
-x-7=9+x
3
1
3
-x-7=9+-x
3
3
-1
-1
+ -x + -x
-2-
numerator and denominator
-3x
Add -6xon
both sides
x=6
The health clubs cost the same for 6 visits per
month.
hours.
+6 +6
-1
9
3x + 20 + - 20 = 6x + 2 + - 20 Add - 20 on
both sides
3x =6x + -18
Combine
constant terms
fractions
150 60
-=-t
60 60
Combine like terms
sides
Combine constantterms
-*-=-*-t
60 1 60 1
Add -20x on bothsides
~*-16=~*~x
2
2 3
-24 = x
Multiply by ~ on both sides'
2
...!....
1.8
Simplify on both sides
Divide -6.8by 1.8
Use theMATH,
a simplified
Frac
fraction
@ Houghton Mifflin Company. All rights reserved.
Section 3.2
13.
c.
1 2
1
-x--=x-3 3
2
-1
-1
+ -x
A Visit to the Movies
y,
20
+ -x
Add
-1
~ IS
-x on bothsides
-L-L
8
3
-2 2
-=-x-332
43
.5 10
~
1 C b lik
om me eterms
'
o
-1
3
-1
2 1
( x+ '3x='3X+ '3x='3X)
Add .!. on both sides
2
(Xl> YI)
1.5
2
2.5 x
(Xz, yz)
(2, '5)
run =Xz
-=-x
6 3
I
Pounds of Candy
19.
1
1
++--1--1
- 1 2
0,5
Cl,3)
-XI = -1 - 2 = -3,
rise = Yz - YI = 3 - '5 = 8
Combine constant terms
21. 3x-4y
when
x =
-1
- andy
3
= 2
C %+~= - ~+%= - ~)
3 - 1 3 2
_* -=-*-x
2
6 2 3
- 1
- =x
4
or x
'
,
MutlPy
1 1 b 0th SIdes by-
3
=3*C ~)-4*2
2
= -1-8
= -.25
=
= -9
15. a. Let h = the number of hours ofInternet use.
provider one: 12 + 2h; provider two: 15 + 1.5h
b. 12+2h=
15 + l.5h
c. 12+2h=15+1.5h
+-1.5h +-1.5h
12+.5h=15
+-12 +-12
.5h=3
1
1
-*.5h =-*3
.5
.5
h=6
Add -1.5h on both sides
Combine like terms
Add -12 on both sides
1
23. 3+8+2*--2
3
4
1
=3+8+2*--8
4
1
=3+4*--8
4
=3+1-8
Cube 2
Divide 8 by 2
Multiply 4 by .!.
4
Combine constant terms
Multiply both sides by .!..
.5
d. Both Internet providers charge the same
amount for 6 hours of use.
Skills and Review 3.1
17. a. Yl=7+5X
b.
.25
.5
.75
1
2
-1 + -8
1.25
9.5
10.75
12
17
117+5X
@ Houghton Mifflin Company. All rights reserved.
-2 1
1
25. b. 5 ='2=-=.04
5
25
None of these equivalent expressions
equal -25