Chapter 1: Equations, Inequalities, and Mathematical Modeling
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
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
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
Solutions Manual for College Algebra 12th Edition By Ron Larson
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 Solutions Manual for College Algebra 12th Edition By Ron Larson
Yes, the point is on the graph.
, Solution and Answer Guide: Larson, College Algebra, 12e, 2027, 9798214407401;
Chapter 1: Equations, Inequalities, and Mathematical Modeling
Solutions Manual for College Algebra 12th Edition By Ron Larson
1.1.7.
?
( )
(a) 1, 5 : 5 = 4 − 1 − 2
?
5 = 4−1
53
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 ?
( ) ( ) + 5 (4) = 8
2
(b) 0, 4 : 2 0
?
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
Solutions Manual for College Algebra 12th Edition By Ron Larson