These techniques involve rewriting problems in the form of symbols. For example, the stated problem "Find a number which, when added to 3, yields 7" may be written as:
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At this point in my career I mostly teach Calculus and Differential Equations.
While there is some review of exponents, factoring and graphing it is assumed that not a lot of review will be needed to remind you how these topics work. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
Because I wanted to make this a fairly complete set of notes for anyone wanting to learn algebra have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here.
Likewise, even if I do work some of the problems in here I may work fewer problems in class than are presented here. Sometimes questions in class will lead down paths that are not covered here. You should always talk to someone who was in class on the day you missed and compare these notes to their notes and see what the differences are.
This is somewhat related to the previous three items, but is important enough to merit its own item. Using these notes as a substitute for class is liable to get you in trouble. As already noted not everything in these notes is covered in class and often material or insights not in these notes is covered in class.
Here is a listing and brief description of the material that is in this set of notes. Preliminaries - In this chapter we will do a quick review of some topics that are absolutely essential to being successful in an Algebra class.
We review exponents integer and rationalradicals, polynomials, factoring polynomials, rational expressions and complex numbers.
Integer Exponents — In this section we will start looking at exponents. We will give the basic properties of exponents and illustrate some of the common mistakes students make in working with exponents. Examples in this section we will be restricted to integer exponents.
Rational exponents will be discussed in the next section. Rational Exponents — In this section we will define what we mean by a rational exponent and extend the properties from the previous section to rational exponents.
We will also discuss how to evaluate numbers raised to a rational exponent. Radicals — In this section we will define radical notation and relate radicals to rational exponents.
We will also give the properties of radicals and some of the common mistakes students often make with radicals. We will also define simplified radical form and show how to rationalize the denominator. Polynomials — In this section we will introduce the basics of polynomials a topic that will appear throughout this course.
We will define the degree of a polynomial and discuss how to add, subtract and multiply polynomials.
Factoring Polynomials — In this section we look at factoring polynomials a topic that will appear in pretty much every chapter in this course and so is vital that you understand it. We will discuss factoring out the greatest common factor, factoring by grouping, factoring quadratics and factoring polynomials with degree greater than 2.
Rational Expressions — In this section we will define rational expressions. We will discuss how to reduce a rational expression lowest terms and how to add, subtract, multiply and divide rational expressions.
Complex Numbers — In this section we give a very quick primer on complex numbers including standard form, adding, subtracting, multiplying and dividing them. Solving Equations and Inequalities - In this chapter we will look at one of the most important topics of the class.
The ability to solve equations and inequalities is vital to surviving this class and many of the later math classes you might take. We will discuss solving linear and quadratic equations as well as applications.
In addition, we will discuss solving polynomial and rational inequalities as well as absolute value equations and inequalities. Solutions and Solution Sets — In this section we introduce some of the basic notation and ideas involved in solving equations and inequalities. We define solutions for equations and inequalities and solution sets.
Linear Equations — In this section we give a process for solving linear equations, including equations with rational expressions, and we illustrate the process with several examples.
In addition, we discuss a subtlety involved in solving equations that students often overlook. Applications of Linear Equations — In this section we discuss a process for solving applications in general although we will focus only on linear equations here.
Equations With More Than One Variable — In this section we will look at solving equations with more than one variable in them. These equations will have multiple variables in them and we will be asked to solve the equation for one of the variables. This is something that we will be asked to do on a fairly regular basis.
Quadratic Equations, Part I — In this section we will start looking at solving quadratic equations.Algebra Practice: Free! Algebra Worksheet Generator - Generate your own algebra worksheets to print and use. Includes many options and types of equations, systems, and quadratics.
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While the 5 steps of Algebra problem solving are listed below, this article will focus on the first step, Identify the problem. FIRST-DEGREE EQUATIONS AND INEQUALITIES. In this chapter, we will develop certain techniques that help solve problems stated in words.
These techniques involve rewriting problems in . Type your algebra problem into the text box. For example, enter 3x+2=14 into the text box to get a step-by-step explanation of how to solve 3x+2= Try this example now! Work through each problem slowly and start by identifying your variables.
Then write an inequality that represents the problem. Once you've written the inequality, the hard work is done and you are ready to solve!