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 LP Courses
 Introductory Algebra

Chapter 1  Equations, Inequalities, Problem Solving

Introduction

1.1 – Simplifying Algebraic Expressions

1.1 – Homework

1.1 – Quiz

1.1 – Additional Problems

1.2 – The Addition Principle of Equations

1.2 – Homework

1.2 – Quiz

1.2 – Additional Problems

1.3 – The Multiplication Principle of Equations

1.3 – Homework

1.3 – Quiz

1.3 – Additional Problems

1.4 – Solving Linear Equations

1.4 – Homework

1.4 – Quiz

1.4 – Additional Problems

1.5 – Problem Solving

1.5 – Homework

1.5 – Quiz

1.5 – Additional Problems

1.6 – Formulas

1.6 – Homework

1.6 – Quiz

1.6 – Additional Problems

1.7 – Percents

1.7 – Homework

1.7 – Quiz

1.7 – Additional Problems

1.8 – Problems Involving Two Unknowns

1.8 – Homework

1.8 – Quiz

1.8 – Additional Problems

Introduction

Assessment 1

Chapter 2  Linear Inequalities and Absolute Value

2.1 – Linear Inequalities in One Variable

2.1 – Homework

2.1 – Quiz

2.1 – Additional Problems

2.2 – Applications of Linear Inequalities

2.2 – Homework

2.2 – Quiz

2.2 – Additional Problems

2.3 – Sets and Compound Inequalities

2.3 – Homework

2.3 – Quiz

2.3 – Additional Problems

2.4 – Equations with Absolute Values

2.4 – Homework

2.4 – Quiz

2.4 – Additional Problems

2.5 – Absolute Value Inequalities

2.5 – Homework

2.5 – Quiz

2.5 – Additional Problems

2.6 – Functions

2.6 – Homework

2.6 – Quiz

2.6 – Additional Problems

2.1 – Linear Inequalities in One Variable

Assessment 2

Chapter 3  Linear Equations with Two Variables

3.1 – Graphs and the Rectangular Coordinate system

3.1 – Homework

3.1 – Quiz

3.1 – Additional Problems

3.2 – Graphing Linear Equations

3.2 – Homework

3.2 – Quiz

3.2 – Additional Problems

3.3 – Graphing Using Intercepts

3.3 – Homework

3.3 – Quiz

3.3 – Additional Problems

3.4 – Slope and Rate of Change

3.4 – Homework

3.4 – Quiz

3.4 – Additional Problems

3.5 – Equations of Lines

3.5 – Homework

3.5 – Quiz

3.5 – Additional Problems

3.6 – Approximate Linear Relationships

3.6 – Homework

3.6 – Quiz

3.6 – Additional Problems

3.7 – Graphing Linear Inequalities of Two Variables

3.7 – Homework

3.7 – Quiz

3.7 – Additional Problems

3.1 – Graphs and the Rectangular Coordinate system

Assessment 3

Chapter 4  Systems of Linear Equations

4.1 – Solving a 2×2 System by Graphing

4.1 – Homework

4.1 – Quiz

4.1 – Additional Problems

4.2 – Solving a 2×2 System by Substitution

4.2 – Homework

4.2 – Quiz

4.2 – Additional Problems

4.3 – Addition/Elimination Method

4.3 – Homework

4.3 – Quiz

4.3 – Additional Problems

4.4 – Applications of Systems of Equations

4.4 – Homework

4.4 – Quiz

4.4 – Additional Problems

4.5 – Solving Systems using Matrices

4.5 – Homework

4.5 – Quiz

4.5 – Additional Problems

4.6 – Graphing Systems of Linear Inequalities in Two Variables

4.6 – Homework

4.6 – Quiz

4.1 – Solving a 2×2 System by Graphing

Assessment 4

Chapter 5  Exponents, Radicals and Polynomials

5.1 – Exponent Properties

5.1 – Homework

5.1 – Quiz

5.2 – Scientific Notation

5.2 – Homework

5.2 – Quiz

5.2 – Additional Problems

5.3 – Radicals

5.3 – Homework

5.3 – Quiz

5.3 – Additional Problems

5.4 – Simplifying Radicals

5.4 – Homework

5.4 – Quiz

5.4 – Additional Problems

5.5 – Problem Solving using Radical Equations

5.5 – Homework

5.5 – Quiz

5.5 – Additional Problems

5.6 – Polynomials

5.6 – Homework

5.6 – Quiz

5.6 – Additional Problems

5.7 – Factoring Polynomials

5.7 – Homework

5.7 – Quiz

5.7 – Additional Problems

5.1 – Exponent Properties

Assessment 5

Chapter 6  Exponential and Logarithmic Functions

6.1 – Exponential Functions

6.1 – Homework

6.1 – Quiz

6.1 – Additional Problems

6.2 – Applications of Exponential Functions

6.2 – Homework

6.2 – Quiz

6.2 – Additional Problems

6.3 – Logarithmic Functions

6.3 – Homework

6.3 – Quiz

6.3 – Additional Problems

6.4 – Common Logarithms

6.4 – Homework

6.4 – Quiz

6.5 – Natural Logarithms

6.5 – Homework

6.5 – Quiz

6.6 – Solving Exponential Equations

6.6 – Homework

6.6 – Quiz

6.6 – Additional Problems

6.7 – Solving Logarithmic Equations

6.7 – Homework

6.7 – Quiz

6.7 – Additional Problems

6.8 – Applications of Logarithmic Functions

6.8 – Homework

6.8 – Quiz

6.8 – Additional Problems

6.1 – Exponential Functions

Assessment 6

Final Exam
1.2 – The Addition Principle of Equations
The Addition Principle of Equalities
Imagine we have a fulcrum and a lever with two objects, one on each end of the lever. The objects are shaped differently, but have the same weight. The lever is in balance.
Now imagine a third object is placed at one side of the lever, but not on the other. What happens?
Our lever falls out of balance. The weights are no longer equal. But if we were to add the same weight to both sides …
We see that we have maintained a balance again, often called an equilibrium.
The same concept can be applied to mathematical equations. In fact, the fulcrum and lever balancing act above is a very important concept in physics, and is modeled by mathematical equations. We will, of course, focus on the mathematical aspects.
Addition Principle of Equalities 

The Addition Principle of Equalities states that if you add the same value to each side of an equation, you maintain the equality. Mathematically, this is: 
Or in other words, if we add the same thing to each side of an equation, we maintain the equation. This can be particularly useful in equations such as:
We can add a number to both sides of this equation. If we choose wisely, we might eliminate the constant and isolate the variable. Let’s add the opposite of to both sides: Simplifying, this becomes And adding by zero leaves x unchanged, so we write: And we have solved this equation! We may wish to check our solution by replacing x with 15 in our original problem. Which is true 
Solve the equation: 

Again, we begin by adding the opposite of the constant to each side: 
Solve the equation: 

Again, we begin by adding the opposite of the constant to each side: Note that adding a negative can be thought of as subtracting: 
We might also have use of the distributive property before utilizing our addition property.
Solve: 

We might also need to use the addition property more than once in an equation.
Solve: 

We start by subtracting from each side so that we have our variable terms on one side of the equation:

Solve: 

Distribute and simplify first, then use the addition property twice: 