Beginning Algebra, 8th edition — by Elayn Martin-Gay | Instructor's Solutions Manual (Ch. 1-9)

INSTRUCTOR’S
SOLUTIONS MANUAL
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Beginning Algebra
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8th edition
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Elayn Martin-Gay
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, Table of Content

Review of Real Numbers
1.1 Study Skill Tips for Success in Mathematics
1.2 Symbols and Sets of Numbers
1.3 Fractions and Mixed Numbers
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1.4 Exponents, Order of Operations, Variable Expressions, and Equations
1.5 Adding Real Numbers
1.6 Subtracting Real Numbers
Mid-Chapter Review: Operations on Real Numbers
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1.7 Multiplying and Dividing Real Numbers
1.8 Properties of Real Numbers
Equations, Inequalities, and Problem Solving
2.1 Simplifying Algebraic Expressions
2.2 The Addition Property of Equality
2.3 The Multiplication Property of Equality
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2.4 Solving Linear Equations
Mid-Chapter Review: Solving Linear Equations
2.5 An Introduction to Problem Solving
2.6 Formulas and Problem Solving
2.7 Percent and Mixture Problem Solving
2.8 Further Problem Solving
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2.9 Solving Linear Inequalities
Graphing
3.1 Reading Graphs and the Rectangular Coordinate System
3.2 Graphing Linear Equations
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3.3 Intercepts
3.4 Slope and Rate of Change
Mid-Chapter Review: Summary on Slope and Graphing Linear Equations
3.5 Equations of Lines
3.6 Functions
Solving Systems of Linear Equations and Inequalities
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4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Addition
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Mid-Chapter Review: Solving Systems of Equations
4.4 Systems of Linear Equations and Problem Solving
4.5 Graphing Linear Inequalities
4.6 Systems of Linear Inequalities
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Exponents and Polynomials
5.1 Exponents
5.2 Adding and Subtracting Polynomials
5.3 Multiplying Polynomials
5.4 Special Products
Mid-Chapter Review: Exponents and Operations on Polynomials
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5.5 Negative Exponents and Scientific Notation
5.6 Dividing Polynomials
Factoring Polynomials
6.1 The Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials of the Form x2 + bx + c
6.3 Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials

, 6.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping
6.5 Factoring Binomials
Mid-Chapter Review: Choosing a Factoring Strategy
6.6 Solving Quadratic Equations by Factoring
6.7 Quadratic Equations and Problem Solving
Rational Expressions
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7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least
Common Denominator
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7.4 Adding and Subtracting Rational Expressions with Unlike Denominators
7.5 Solving Equations Containing Rational Expressions
Mid-Chapter Review: Summary on Rational Expressions
7.6 Proportion and Problem Solving with Rational Equations
7.7 Variation and Problem Solving
7.8 Simplifying Complex Fractions
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Roots and Radicals
8.1 Introduction to Radicals
8.2 Simplifying Radicals
8.3 Adding and Subtracting Radicals
8.4 Multiplying and Dividing Radicals
Mid-Chapter Review: Simplifying Radicals
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8.5 Solving Equations Containing Radicals
8.6 Radical Equations and Problem Solving
8.7 Rational Exponents
Quadratic Equations
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9.1 Solving Quadratic Equations by the Square Root Property
9.2 Solving Quadratic Equations by Completing the Square
9.3 Solving Quadratic Equations by the Quadratic Formula
Mid-Chapter Review: Summary on Solving Quadratic Equations
9.4 Complex Solutions of Quadratic Equations
9.5 Graphing Quadratic Equations
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Appendices
Geometry
Additional Exercises on Proportion and Proportion Applications
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Operations on Decimals
Mean, Median, Range and Introduction to Statistics/Mode
Tables
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, Chapter 1
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Section 1.2 Practice Exercises 12 12
c. 3= since simplifies to 3.
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1. a. 5 < 8 since 5 is to the left of 8 on the number
line. 7. a. |−8| = 8 since −8 is 8 units from 0 on a
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number line.
b. 6 > 4 since 6 is to the right of 4 on the
number line. b. |9| = 9 since 9 is 9 units from 0 on a number
line.
c. 16 < 82 since 16 is to the left of 82 on the
number line.
c. |−2.5| = 2.5 since −2.5 is 2.5 units from 0 on
a number line.
2. a. 9 ≥ 3 is true, since 9 > 3 is true.
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b. 3 ≥ 8 is false, since neither 3 > 8 nor 3 = 8 is 5 5 5 5
d. = since is unit from 0 on a
true. 11 11 11 11
number line.
c. 25 ≤ 25 is true, since 25 = 25 is true.
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d. 4 ≤ 14 is true, since 4 < 14 is true. e. − = since − is unit from 0 on a
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3. a. 3<8 number line.

b. 15 ≥ 9 8. a. |8| = |−8| since 8 = 8.

c. 6≠7 b. |−3| > 0 since 3 > 0.
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4. The integer −10 represents 10 meters below sea c. |−7| < |−11| since 7 < 11.
level.
d. |3| > |2| since 3 > 2.
5. a. The natural number is 25.
e. |0| < |−4| since 0 < 4.
b. The whole number is 25.
Vocabulary, Readiness & Video Check 1.2
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c. The integers are 25, −15, −99.
1. The whole numbers are {0, 1, 2, 3, 4, ...}.
7 3 2. The natural numbers are {1, 2, 3, 4, 5, ...}.
d. The rational numbers are 25, , −15, − ,
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−3.7, 8.8, −99. 3. The symbols ≠, ≤, and > are called inequality
symbols.
e. The irrational number is 5.
4. The integers are {..., −3, −2, −1, 0, 1, 2, 3, ...}.
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f. The real numbers are 25, , −15, − , 5. The real numbers are {all numbers that
3 4 correspond to points on a number line}.
5, −3.7, 8.8, −99.
6. The rational numbers are
6. a. 0 < 3 since 0 is to the left of 3 on a number a 
line.  a and b are integers, b ≠ 0  .
b 
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b. 15 > −5 since 15 is to the right of −5 on a
7. The irrational numbers are {nonrational numbers
number line.
that correspond to points on a number line}.


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