
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

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

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

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

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

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

Assessment 6

Final Exam
1.4 – Solving Linear Equations
Solving Linear Equations
A Linear Equation is an equation that involves a single variable to the first power. All of the equations we dealt with in the previous sections were linear equations. Here, we will devise a general strategy for solving linear equations.
Solving Linear Equations 


Let’s view this process through a few examples:
Solve: 

Because there are no fractions here, we can skip step 1 and go directly to step 2. We distribute: Then we simplify each side of the equation (step 3): And then get all values onto one side. here it is easy to get them to the left by subtracting from each side. We will also move the non term to the other side by subtracting the 6: We can now also skip step 5, since has been completely isolated. We will then check our solution in the original equation (step 6): 
Solve: 

Again, there are no fractions, so we skip to step 2, distributing gives: Combining like terms yields: it is easy to isolate the variable terms onto the left side of the equation, and the nonvariable terms onto the right. Doing so yields: And finally, solving the equation for x by dividing each side by 6 yields: Which can be simplified to: We can check this by putting it into the original equation: 
Some problems with fractions will require us to deal with them first (Step 1):
Solve: 

In this example we have fractions to deal with, so we use step 1, and multiply each side by the LCD which is 12: The twelve gets distributed through on each side, and we can write it as an improper fraction if we wish: And simplifying: yields: There is no need to remove parentheses, so we skip step 2, and there is also no need to simply each side, so we can skip step 3. We will, however, move all terms to one side of the equation. If we move them to the right side, we can avoid having a negative term: And then using the multiplication principle: Checking this answer by substituting into the original equation will be left to the student. 
When there is a fraction on the outside of a parentheses, it might make the problem easier to distribute first:
Solve: 

Our LCD here is 10, so we multiply every term by 10: and simplify: 
There are, on occasion, equations without solutions:
Solve: 

Going through the general strategy, we have: At this point, when we try to isolate our term, we find that both terms will cancel out, and we are left with: this is a blatantly false statement. When our algebra results in a false statement such as this, then the statement will be false no matter what value of we substitute, so there are no solutions. We might note this with the symbol 
Then there are solutions that have an infinite number of solutions.
Solve: 

Again, through the general strategy, we have: And we can see at this point that the expression on the left is the same as the one on the right. If we try to further isolate terms, we will again eliminate them completely: In this case, however, we come to a completely true statement, and no value of will ever make this untrue. This is called an identity. The solution to this equation is all real numbers. This is often indicated by the use of the symbol 
The last type of equation in this section is those with a variable in the denominator. These problems will be treated with the same process from above. Eliminate the fractions by multiplying by the lowest common denominator. Let us view an example of this:
Solve the equation for : 

The start, the lowest common denominator is multiplied. In this case, the lowest common denominator is . On the left side of the equation, cancels out. On the right hand side, the 3 can distribute: Subtract from each side to get the terms to one side: and then subtract 6 from each side to isolate the term: And finally, divide each side by 2: 
Solve the equation for 

The lowest common denominator in this equation is the product of both denominators: . This is multiplied to both sides of the equation: The likefactors cancel: Leaving a factor on each side: Distributing on both sides: Moving terms to the right by subtracting : And moving the nonvariable terms to the left by subtracting 6: And finally dividing each side by 2 gives 