Basic Algebra Topics

Good news: you've 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're going to work with now are just...

Let's get down to business. An expression is made up of terms. Terms are the separate values in an expression. Each term can be a variable, a number and a variable, or a number and many variables w...

Expressions are made of variables, or letters that take the place of unknown numbers. But what if we know the numbers? We can take out the variable, replace it with the number, and do the math. Thi...

Algebraic terms can, and often should, be combined and simplified. However, only terms that are "like," meaning that they have the exact same variables and hairdo, can be added or subtracted....

Long ago, and in a guide far, far away, we learned the properties of numbers: commutative, associative, distributive, inverse, and identity. These properties also apply to adding and multiplying w...

This one is insanely important when working with algebraic expressions. The distributive property basically says this:andHowever, the distributive property does not work when the variables inside t...

A polynomial is an expression that's made up of constants and/or variables. All the expressions we've been dealing with so far have been polynomials: 5x + 17 and 18xy2 – 17xy + 19y are both polyn...

This is the last type of multiplication that we're going to look at in this unit. The good news is that there's nothing new to learn here. All we're really doing is applying the distributive prope...

Dividing polynomials starts with dividing monomials, and dividing monomials boils down to reducing fractions, and reducing fractions? Pshaw, we've been doing that for eons. No big whoop. The fracti...

Finally, we're getting into the kinds of problems that most people usually think of when they imagine algebra: the ones where we solve for x.There's one extremely important rule to follow when solv...

Solving two-step equations isn't much more complicated than solving one-step equations; it just involves an extra step. Usually, there's more than one way to solve these. It's okay to use what...

This multi-step business may be a bit more complicated than what we've already been doing, but it's nothing we can't handle. It just involves three or more of the same kinds of steps.We've already...

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 equat...

Sometimes we'll need to solve an equation that has a funky answer, like 10 = 8 or y = y. This doesn't necessarily mean that we did anything wrong; it might very well mean that all or no number...

Let's review a math rule. Remember this one? No dividing by zero. Nuh-uh, no way, never, ever. Don't do it. Ever wonder why?A division problem can be read as a multiplication problem that's missi...

Some words can be translated into math, and some math can be translated into words, and neither require the babel fish from The Hitchhiker's Guide to the Galaxy. When we translate words to math, m...

Audrey II is a man-eating plant living in the Little Shop of Horrors and it needs blood, and lots of it. Luckily its caretaker, Seymour, has discovered a blood substitute to feed Audrey II. Now tha...

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

Solving inequalities isn't that much different than solving equations. Instead of having an equal sign divide the two sides, there's an inequality sign. However, there's one really important...

Inequalities, like equations, can be translated and used to solve problems. We use an inequality for values that aren't the same, or that can only be the same up to a certain amount. When a proble...

Chances are, we've been graphing points for a long time. However, we've probably been doing so on charts that look like this:But since we're blasting ahead in math, we'll soon be graphing on chart...

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

We know that we can graph a linear equation with two variables, such as the famous x and y, as a straight line. (By the way: that's true only because the variables don't have any exponents, but tha...

The slope of a line measures its steepness; the larger the absolute value of the slope, the steeper the line is. If we don't know the slope, it's usually represented by the variable m. Why? Maybe...

The x- and y-intercepts of a line are the points where the line intercepts, or crosses, either the x-axis or the y-axis.x-intercept: the point where the line crosses the x-axis. Notice that the y-...

If the equation of a line is in slope-intercept form, it looks like this: y = mx + bHere's what those extra letters mean:m is the slope of the line.b is the y-intercept.Let's look at a few example...

We've now worked pretty extensively with equations containing two variables. All the equations we've looked at so far have represented straight lines, so we call them linear equations. There are se...

Occasionally we'll be given two linear equations, also known as a system of linear equations, and asked to solve for x and y. There are tons of different ways to solve a system of linear equatio...

We can find the solution to a system of linear equations by graphing like a boss, but there are other ways, too. We'll get into these other methods in more detail when we're past pre-algebra, but h...