# Basic Algebra

# Basic Algebra Topics

#### Arithmetic, Geometric & Exponential Patterns

You have actually been working with algebra since you were three and began to notice patterns (red dog, blue cat, red dog, blue cat…). The patterns we are going to work with now are just a littl...

#### Algebraic Expressions

Okay, let's clear this up:An equation is a complete mathematical sentence that includes a sign of equality (like an equal sign). An expression is a mathematical sentence; it doesn't h...

#### Evaluating Algebraic Expressions

To evaluate an algebraic expression, just plug numbers into the expression and simplify it. Don't Forget: you will need your faithful friend PEMDAS (aka Order of Operations).

#### Combining Like Terms

Algebraic terms can, and often should, be combined and simplified. However, only terms that are "like", meaning that they have the exact same variables in each of them, can be added or subtract...

#### Distributive Property

Let's review the properties using variables instead of numbers:AdditionMultiplicationCommutative Associative Inverse Identity The properties above do NOT work with subtr...

#### Multiplying Monomials

You have already started multiplying polynomials, but now we will take this a few steps further. Look at the examples carefully and make note of the exponents. Remember: 5xy means Again,...

#### Multiplying Binomials

This is the last type of multiplication that we are going to learn in this unit. The good news is that there is nothing new to learn here. This is just applying the distributive property twice!...

#### Dividing Polynomials

Dividing polynomials can be a very complicated task, but not to worry, you will be able to handle these well if you follow the examples below. The most important thing to remember is that when you...

#### Graphing X-Y Points

Graphing X-Y PointsChances are you have been graphing points for a long time. However, you may have been doing so on charts that look like this:But since you are blasting ahead in math, you soo...

#### Solving One-Step Equations

Solving One-Step EquationsFinally we are getting into the kinds of problems that you usually think of when you imagine algebra, the ones where you solve for x.There is one extremely important rule...

#### Solving Two-Step Equations

Solving two-step equations is not much more complicated than solving one-step equations; it just involves an extra step. Usually there is more than one way to solve these. It's ok to use whate...

#### Solving More Complex Equations

This multi-step business is not at all more complicated than what you've already been doing. It just involves three or more of the same kinds of steps.Again, it is probably best to isolate the...

#### Solving Equations with Variables on Both Sides

If you encounter a variable on both sides of the equal sign, don't assume it's a typo and move on to the next problem; it may very well be there on purpose. The key to solving these types of e...

#### Solving Funky Equations

Sometimes you will solve an equation that has a funky answer, like 10 = 8 or y = y. This doesn't necessarily mean that you did anything wrong, it might very well mean that all or no numbers wo...

#### Graphing Inequalities

Inequalities are exactly like they sound, equations where the sides are "inequal" (not equal) to each other. There are five basic inequalities that you need to be familiar with:SymbolMeaninggreate...

#### Solving Inequalities

Solving inequalities is not that much different than solving equations. Instead of having an equal sign divide the two sides, there is an inequality sign.
However, there is one really importa...

#### Graphing Lines

You've now worked pretty extensively with equations containing one variable. We are now going to briefly work with ones involving two variables, x and y. Equations that have an x term and a y ter...

#### Intercepts

The x and y-intercepts of a line is the point where the line intercepts, or crosses, either the x-axis or the y-axisX-Intercept: when the line crosses the x-axis, the y value is 0Y-Intercept: Wh...

#### Graphing Horizontal & Vertical Lines

Before we get into the complexities of graphing lines, we are going to first introduce how to graph the really simple lines, those that are completely vertical or horizontal. Take a look at th...

#### Graphing Lines By Plotting Points

Most of the lines you will be graphing will much more complex than simple vertical and horizontal lines. There are many ways to go about graphing these, but we will only work with the two most comm...

#### Slope-Intercept Form

Another way to graph a line is to get it in slope-intercept form: y = mx + b, wherem is the slope of the line b is the y-interceptSince we are given a point of the line, and the slope, we c...

#### Solving Multiple Equations by Graphing

Occasionally you will be given two linear equations and asked to solve for x and y. There are numerous ways to do this, including graphing the lines, substitution, and elimination. However, in pr...