Basic Algebra Exercises

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...

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....

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...

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...

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...

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...

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...

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...

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...