1. Equations and Inequalities
College Algebra
Chapter 1
Equations and Inequalities

2. Solving equations using
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Solving equations using
Addition and multiplication properties of equality

3. Solving equations using
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Solving equations using
Addition and multiplication properties of equality
General Approach
Simplify the equation
Clear fractions or decimals as needed/desired
Combine any like terms
Solve the equation
Use additive property of equality to write the
equation with all variable terms on one side
and constants on the other
Simplify each side
Use the multiplicative property of equality to
obtain solution form

4. Solving equations using
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Solving equations using
Addition and multiplication properties of equality
General Approach
Simplify the equation
Clear fractions or decimals as needed/desired
Combine any like terms
Solve the equation
Use additive property of equality to write the
equation with all variable terms on one side
and constants on the other
Simplify each side
Use the multiplicative property of equality to
obtain solution form

5. Solving equations using
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Solving equations using
Addition and multiplication properties of equality
General Approach
Simplify the equation
Clear fractions or decimals as needed/desired
Combine any like terms
Solve the equation
Use additive property of equality to write the
equation with all variable terms on one side
and constants on the other
Simplify each side
Use the multiplicative property of equality to
obtain solution form

6. Linear Equation Terminology
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Linear Equation Terminology
Algebraic expression
Equation
Linear equations
Standard form
Conditional equation
Identity
Contradictions
Sum or difference of algebraic terms
Statement that two expressions are equal
Three tests – exponents, divisors, multiplication
Ax+By=C, where A and B are not both zero
Equation is true for one value and false for all others
Equation that is always true
Equations that are never true

7. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
No Solution

8. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving

9. Linear Equation Terminology
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Linear Equation Terminology
Literal equation
Formula
An equation that has two or more unknowns
Equation that models a known relationship between two or more quantities

10. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Literal Equations:

11. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Literal Equations:

12. Consecutive Integer Problems
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Consecutive Integer Problems
Sum of 3 even integers is 66. What are they?

13. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Mixture Problems

14. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Mixture Problems

15. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving

16. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving

17. College Algebra Chapter 1
College Algebra Chapter 1.1 Linear Equations, Formulas, and Problem Solving
Homework pg

18. Inequalities and Solution Sets Terminology
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Inequalities and Solution Sets Terminology
Solution Set
Set Notation
Number Line
Interval Notation
Boundary Point
Inclusion
Not Included
The set of numbers that satisfy an inequality
Method of writing a solution set. Ex {x|x>k}
Method of writing a solution set
Method of writing a solution set. Ex
Marks the location of a number on a number line also called an endpoint
Uses brackets [ ] to indicate
Uses parenthesis ( ) to indicate

19. Inequalities and Solution Sets Terminology
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Inequalities and Solution Sets Terminology
Set Notation
The set of all n
Such that
n is greater than or equal to 1

20. Inequalities and Solution Sets Terminology
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Inequalities and Solution Sets Terminology
Interval Notation
n is an element of
This set
Smaller number to left
Larger number to right
[,] brackets if boundary points is included
(,) parenthesis if boundary point is not included

21. Write the following in set notation, number line graph,
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Write the following in set notation, number line graph,
and interval notation
x is less than 10
Set notation
Number line graph 10
Interval notation

22. Write the following in set notation, number line graph,
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Write the following in set notation, number line graph,
and interval notation
n is greater than or equal to 2
Set notation
Number line graph 2
Interval notation

23. Write the following in set notation, number line graph,
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Write the following in set notation, number line graph,
and interval notation
X is less than 5 and greater than or equal to -1
Set notation
Number line graph -1 5
Interval notation

24. Solving Inequalities Beware of multiplying or dividing by a (-)
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Solving Inequalities
Beware of multiplying or dividing by a (-)

25. College Algebra Chapter 1.2 Linear Inequalities in One Variable
Solving Inequalities

26. Solving Compound Inequalities
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Solving Compound Inequalities

27. Solving Compound Inequalities
College Algebra Chapter 1.2 Linear Inequalities in One Variable
Solving Compound Inequalities

28. College Algebra Chapter 1.2 Linear Inequalities in One Variable
Homework pg

29. College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Zero factor property
Given that A and B represent real numbers or real-valued expressions, if , then either

30. Remove common factors aka undistribute
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solve
Set equal to zero
Remove common factors aka undistribute
Factor trinomial
Solve each factor equal to zero

31. College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solve

32. College Algebra Chapter 1.3 Solving Polynomial and Other Equations

33. Solving rational equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving rational equations
Identify and exclude values that cause a zero denominator
Multiply by the LCD and simplify
Solve resulting equation
Check in original equation and step 1

34. Solving rational equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving rational equations
Identify and exclude values that cause a zero denominator
Multiply by the LCD and simplify
Solve resulting equation
Check in original equation and step 1

35. Solving rational equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving rational equations
Identify and exclude values that cause a zero denominator
Multiply by the LCD and simplify
Solve resulting equation
Check in original equation and step 1

36. Solving rational equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving rational equations
Identify and exclude values that cause a zero denominator
Multiply by the LCD and simplify
Solve resulting equation
Check in original equation and step 1

37. Solving rational equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving rational equations
Identify and exclude values that cause a zero denominator
Multiply by the LCD and simplify
Solve resulting equation
Check in original equation and step 1

38. Solving Radical Equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving Radical Equations
Isolate radical term
Square both sides
Simplify

39. 3 Solving Radical Equations Isolate radical term Square both sides
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving Radical Equations
Isolate radical term
Square both sides
Simplify 3

40. Solving Radical Equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving Radical Equations
Isolate radical term
Square both sides
Simplify

41. Solving Radical Equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving Radical Equations
Isolate radical term
Square both sides
Simplify

42. Solving Radical Equations
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving Radical Equations
Isolate radical term
Square both sides
Simplify

43. College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Rational Exponents 15

44. College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Rational Exponents

45. Solving with U-Substitution
College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Solving with U-Substitution

46. College Algebra Chapter 1.3 Solving Polynomial and Other Equations
Homework pg

47. Imaginary unit i represents the number whose square is -1
College Algebra Chapter 1.4 Complex Numbers
Imaginary unit i represents the number whose square is -1

48. College Algebra Chapter 1.4 Complex Numbers

49. College Algebra Chapter 1.4 Complex Numbers
Complex numbers are those that can be written in the form , where a and b are real numbers and The expression is called the standard form of a complex numbers
Real part
Imaginary part

50. Identify the values of a and b
College Algebra Chapter 1.4 Complex Numbers
Identify the values of a and b
a=-5 b=3
-5+3i
2-3i
a=2 b=-3
a=2 b=7
a=0 b=
a=7 b=0 7

51. Identify the values of a and b
College Algebra Chapter 1.4 Complex Numbers
Identify the values of a and b
a=0.2 b=0.75

52. Adding and subtracting complex numbers
College Algebra Chapter 1.4 Complex Numbers
Adding and subtracting complex numbers

53. Adding and subtracting complex numbers
College Algebra Chapter 1.4 Complex Numbers
Adding and subtracting complex numbers

54. Multiplying Complex Numbers
College Algebra Chapter 1.4 Complex Numbers
Multiplying Complex Numbers

55. Multiplying Complex Numbers
College Algebra Chapter 1.4 Complex Numbers
Multiplying Complex Numbers

56. Multiplying by the Complex Conjugate
College Algebra Chapter 1.4 Complex Numbers
Multiplying by the Complex Conjugate

57. Division of Complex Numbers
College Algebra Chapter 1.4 Complex Numbers
Division of Complex Numbers

58. College Algebra Chapter 1.4 Complex Numbers
Homework pg

59. Standard Form and Coefficients
College Algebra Chapter 1.5 Non-factorable Quadratic Equations
Standard Form and Coefficients
a=2 b=0 c=-10
a=-3 b=1 c=-12
a= b= c=0
Not quadratic

60. College Algebra Chapter 1.5 Non-factorable Quadratic Equations
Square root property

61. College Algebra Chapter 1.5 Non-factorable Quadratic Equations
solve

62. College Algebra Chapter 1.5 Non-factorable Quadratic Equations
solve

63. Completing the Square Subtract the constant c from both sides
College Algebra Chapter 1.5 Non-factorable Quadratic Equations
Completing the Square
Subtract the constant c from both sides
Divide both sides by the leading coefficient a
Take and add the result to both sides
Factor the left hand side as a binomial square: simplify the right hand side
Solve using the SQR property of equality

64. College Algebra Chapter 1.5 Non-factorable Quadratic Equations
Completing the Square
Subtract the constant c from both sides
Divide both sides by the leading coefficient a
Take and add the result to both sides
Factor the left hand side as a binomial square: simplify the right hand side
Solve using the SQR property of equality

65. Quadratic Formula Discriminant 1 real root 2 real roots
College Algebra Chapter 1.5 Non-factorable Quadratic Equations
Quadratic Formula
Discriminant
1 real root
2 real roots
2 complex roots

66. Quadratic Formula Solve No Solution
College Algebra Chapter 1.5 Non-factorable Quadratic Equations
Quadratic Formula
Solve
No Solution

67. Quadratic Formula Solve {6,-3} {6,1}
College Algebra Chapter 1.5 Non-factorable Quadratic Equations
Quadratic Formula
Solve
{6,-3}
{6,1}

68. College Algebra Chapter 1.5 Non-factorable Quadratic Equations
Homework pg

69. Solve -10 No Solution All Real Numbers 2
College Algebra Chapter 1 Review
Solve
-10
No Solution
All Real Numbers 2

70. Solve and graph, state solution in set and interval notation
College Algebra Chapter 1 Review
Solve and graph, state solution in set and interval notation

71. Solve by the method of your choice
College Algebra Chapter 1 Review
Solve by the method of your choice
{5, -5}
{7.483, }
{5/8, -8/5}
{2/7, -7}
{8, 7}
{-4, 6}
{0.732, }
No solution
{1.309, }
{12.426, }

72. College Algebra Chapter 1 Review
Solve
{6}
{3}
{-1}
{9, 2}

73. College Algebra Chapter 1 Review
Homework pg