Solutions Manual for College Algebra 12th Edition by Ron Larson

Solution and Answer Guide: Larson, College Algebra, 12e, 2027, 9798214407401;
Chapter 1: Equations, Inequalities, and Mathematical Modeling




Solution and Answer Guide
LARSON, COLLEGE ALGEBRA, 12E, 2027, 9798214407401;
CHAPTER 1: EQUATIONS, INEQUALITIES, AND MATHEMATICAL MODELING


TABLE OF CONTENTS
Section 1.1 Graphs of Equations ........................................................................................ 95
Section 1.2 Linear Equations in One Variable ................................................................. 109
Section 1.3 Modeling with Linear Equations .................................................................. 129
Section 1.4 Quadratic Equations and Applications ........................................................ 145
Section 1.5 Complex Numbers .......................................................................................... 181
Section 1.6 Other Types of Equations ............................................................................. 192
Section 1.7 Linear Inequalities in One Variable .............................................................. 225
Section 1.8 Other Types of Inequalities .......................................................................... 239
Review Exercises for Chapter 1 ....................................................................................... 272
Problem Solving for Chapter 1 ......................................................................................... 303




© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 94
accessible website, in whole or in part.

, Solution and Answer Guide: Larson, College Algebra, 12e, 2027, 9798214407401;
Chapter 1: Equations, Inequalities, and Mathematical Modeling


SECTION 1.1 GRAPHS OF EQUATIONS
1.1.1.
solution or solution point
1.1.2.
graph

1.1.3.
Three approaches to solve problems mathematically are algebraic, graphical,
and numerical.

1.1.4.

( )
Let x, y be any point on the circle. The distance between the center h, k ( )
and ( x, y ) is the radius r. So, ( x − h) + ( y − k )
2 2
= r.

1.1.5.
?
( ) () ()
2
(a) 2, 0 : 2 − 3 2 + 2=0
?
4 − 6 + 2=0
0=0
Yes, the point is on the graph.
?
( ) ( ) ( )
2
(b) −2, 8 : −2 − 3 −2 + 2 = 8
?
4+6+2 =8
12  8
No, the point is not on the graph.
1.1.6.
?
( )
(a) 0, 2 : 2 = 0 + 4
2=2
Yes, the point is on the graph.
?
( )
(b) 5, 3 : 3 = 5+4
?
3= 9
3=3
Yes, the point is on the graph.




© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 95
accessible website, in whole or in part.

, Solution and Answer Guide: Larson, College Algebra, 12e, 2027, 9798214407401;
Chapter 1: Equations, Inequalities, and Mathematical Modeling


1.1.7.
?
( )
(a) 1, 5 : 5 = 4 − 1 − 2
?
5 = 4−1
53
No, the point is not on the graph.
?
( )
(b) 6, 0 : 0 = 4 − 6 − 2
?
0 = 4−4
0=0
Yes, the point is on the graph.
1.1.8.
2 ?
( ) ( ) + 5 (0 ) = 8
2
(a) 6, 0 : 2 6
?
2 ( 36) + 5 (0) = 8
?
72 + 0 = 8
72  8
No, the point is not on the graph.
2 ?
( ) ( ) ( )
2
(b) 0, 4 : 2 0 +5 4 = 8
?
2 (0) + 5 ( 16) = 8
?
0 + 80 = 8
80  8
No, the point is not on the graph.
1.1.9.
y = −2x + 5
5
x −1 0 1 2
2
y 7 5 3 1 0

5 
( x, y ) ( −1, 7) (0, 5) ( 1, 3) (2, 1)  , 0
2 




© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 96
accessible website, in whole or in part.

, Solution and Answer Guide: Larson, College Algebra, 12e, 2027, 9798214407401;
Chapter 1: Equations, Inequalities, and Mathematical Modeling




1.1.10.
3
y= x−1
4
4
x −2 0 1 3
2

5 1 1
y − –1 − 0
2 4 2
 5  1 4   1
( x, y )  −2, − 
2
(0, − 1)  1, − 
4
 , 0  2, 
  3   2




1.1.11.

y = x 2 − 3x
x −1 0 1 2 3
y 4 0 –2 –2 0

( x, y ) ( −1, 4) (0, 0) ( 1, − 2) (2, − 2) (3, 0)




© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 97
accessible website, in whole or in part.