James A Sellers

Explore linear equations, starting with one-step equations and then advancing to those requiring two or more steps to solve. Next, apply the distributive property to simplify certain problems, and then learn about the three categories of linear equations.

One of the most important skills related to quadratics is factoring. Review the basics of factoring, and learn to recognize a very useful special case known as the difference of two squares. Close by working on a word problem that translates into a quadratic equation.

Continuing your exploration of rational expressions, try your hand at multiplying and dividing them. The key to solving these complicated-looking equations is to proceed one-step at a time. Close the lesson with a problem that brings together all you've learned about rational functions.

The order in which you do simple operations of arithmetic can make a big difference. Learn how to solve problems that combine adding, subtracting, multiplying, and dividing, as well as raising numbers to various powers. These same concepts also apply when you need to simplify algebraic expressions, making it critical to master them now.

Investigating more complicated examples of linear equations, learn that linear equations fall into three categories. First, the equation might have exactly one solution. Second, it might have no solutions at all. Third, it might be an identity, which means every number is a solution.

Pascal's triangle is a famous triangular array of numbers that corresponds to the coefficients of binomials of different powers. In an episode connecting a branch of mathematics called combinatorics with algebra, investigate the formula for each value in Pascal's triangle, the factorial function, and the binomial theorem.

Explore two other techniques for solving systems of two linear equations. First, the method of substitution solves one of the equations and substitutes the result into the other. Second, the method of elimination adds or subtracts the equations to see if a variable can be eliminated.

Shift gears to consider linear inequalities, which are mathematical expressions featuring a less than sign or a greater than sign instead of an equal sign. Discover that these kinds of problems have some very interesting twists, and they come up frequently in business applications.

In this lesson, work through simple one- and two-step linear equations, learning how to isolate the variable by different operations. Professor Sellers also presents a word problem involving a two-step equation and gives tips for how to solve it.

Linear equations reflect the behavior of real-life phenomena. Practice evaluating tables of numbers to determine if they can be represented as linear equations. Conclude with an example about the yearly growth of a tree. Does it increase in size at a linear rate?