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Interval Notation

Rather than write x > 5 or -2 < x < 4, we're going to put the numbers in parentheses and brackets, like (2,6) or [-3,1). The only trick: whether to use ( )'s or [ ]'s or some combination of the two! You'll also have to learn how to draw the infinity symbol super-good (lol).

This video appears on the page: Solving Inequalities ,Pre-Algebra Class Page ,Set Builder Notation

Solving Inequalities with just X

In this video we'll solve problems like 3x+4<7 and x-2>2. What do these problems have in common? Just X, no Y! So when we graph the answer, we'll do that on a number line. I also discuss the exciting topic of how to decide whether to use an "open" or "closed" dot.

This video appears on the page: Solving Inequalities

Solving Linear Inequalities & Interval Notation
Solving Inequalities with just x
Interval Notation
Systems of Inequalities (with just x)
Linear Inequalities with both x & y
Systems of Inequalities with both x & y

Inequalities are just equations with an "<" or ">" instead of "=". In this chapter, we'll look at how to solve a few different types of "linear" inequalities: ones with just X, where you present the answer in Interval Notation, and ones with X & Y, where you shade one side of the line or another. We'll also cover systems of inequalities, "and" vs "or", etc. For other types of inequalities, try this page.

Part of the course(s): College Algebra ,Algebra 2 ,Algebra

Finding the Intersection of Lines (the graphing method)

While doing your systems homework, you probably noticed that they usually used x and y as the two variables. That wasn't a coincidence. Turns out that the answers you get are the point of intersection of the lines if you had graphed them.

This video appears on the page: Solving Systems of Equations

Solving 3 Simultaneous Equations with 3 Unknowns

These take a lot longer than the two-equation problems, but they aren't so bad. In this video I show you step-by-step how to get it done quick, and I also show you how to tackle the tricky problem every teacher uses: leaving a variable or two out of some of the equations.

This video appears on the page: Solving Systems of Equations

Solving Systems of Simultaneous Equations with Substitution

Most kids I tutor dislike this method, preferring elimination. Quite frankly, so do I. But sometimes elimination is too hard because the numbers don't work out, or there are fractions involved, or the teacher's instructions demand substitution. In this video, I try to make it make sense.

This video appears on the page: Solving Systems of Equations

Solving Systems of Simultaneous Equations with Elimination

Elimination is the "canceling" method of solving two equations with two unknowns, in which you add or subtract the two equations to try and cancel one of the variables. In this video I do a few examples, from easy to hard.

This video appears on the page: Solving Systems of Equations

Solving Systems of Equations (2 or 3 equations at once)
Solving Systems of Equations with Substitution
Solving Systems w/ Elimination (addition, subtraction)
Solving 3 Simultaneous Equations with 3 Unknowns
Finding the Intersection of Lines (the graphing method)

Whenever you're given two or three equations at the same time, they're "simultaneous equations. This chapter covers "elimination" and "substitution" techniques to solve for X & Y, and explains finding the intersection of lines (or not as in the case of parallel & coincident lines). I also demonstrate solving three equations, three unknowns.

Part of the course(s): College Algebra ,Algebra 2 ,Algebra

Imaginary Numbers & Square Roots of Negatives

Up to now, we weren't allowed to take the square root of negative numbers. And you still aren't. Except in this chapter, where "i" will come into your life and then hurry away just once you're getting to know him, with perhaps a quick reprise on the midterm.

This video appears on the page: Imaginary & Complex Numbers

Complex Numbers

When an imaginary number and a real number walk into a bar, what do you get? A complex situation. And a dumb joke. Point is that complex numbers are stuff like 3+2i and 2-2i, and in this video I get into how to multiply them, divide them, and rationalize them.

This video appears on the page: Imaginary & Complex Numbers

Imaginary & Complex Numbers
Imaginary Numbers & Square Roots of Negatives
Complex Numbers

All is not as it seems in this exciting and short chapter. We're talking square roots of negative numbers, finding high exponents of "i" like i27, and rationalizing imaginary and complex denominators.

Part of the course(s): Math Analysis ,College Algebra ,Algebra 2 ,Pre-Calculus

Rational Exponents (a.k.a. fractions upstairs)

Fractions in the exponent are despised by almost every student I've ever tutored in this class. And I'm not going to change anyone's mind about that. But you can get through them with a little less trouble if you follow these steps.

This video appears on the page: Roots and Rational Exponents

Dividing Roots & Rationalizing Denominators

Like Martha Stewart and your butler, mathematicians are sticklers for manners. Unlike Martha and Jeeves, mathematicians (and thus your teacher) object to radicals in the denominator. Why? I doubt even they know.

This video appears on the page: Roots and Rational Exponents

Adding & Multiplying Roots

Similarly to when you're combining "like terms" in equations, adding and subtracting roots requires the same number under the radical.

This video appears on the page: Roots and Rational Exponents

Variables Under Radicals

What happens when you put x's and y's under the square root sign along with the numbers? It's not as bad as you think.

This video appears on the page: Roots and Rational Exponents

Simplifying Roots & Radicals

This video starts things off on the right foot with square roots, demonstrating the easiest and hardest-to-mess-up method for simplifying radicals, which is where we try and get the smallest number under the root as possible.

This video appears on the page: Pythagorean Theorem ,Roots & Radicals ,Roots and Rational Exponents ,ACT Prep free videos ,free Accuplacer prep videos ,TCI free videos ,SAT Free Videos

Roots, Radicals, Rationalizing Denominators, & Rational Exponents
Simplifying Roots & Radicals
Variables Under Radicals
Adding & Multiplying Roots
Dividing Roots & Rationalizing Denominators
Rational Exponents (a.k.a. fractions upstairs)

This chapter covers everything you'll ever be asked to do to or with a root or a "rational" (fraction) exponent. Topics covered: simplifying roots & radicals, reducing roots, dividing roots, adding-subtracting-multiplying-and-dividing radicals, and rationalizing denominators.

Part of the course(s): Math Analysis ,College Algebra ,Algebra 2 ,Pre-Calculus

Factoring by Grouping

Factoring by grouping is annoying because it only works on problems that are carefully contrived by your teacher. Unlike most types of factoring, once you're out of the factoring chapter you'll never see grouping again, so figure out your teacher's pet problems, then move on.

This video appears on the page: Factoring

Factoring Sum & Difference of Cubes

This video is about a rarely-seen factoring situation: cubes. I give you the formula to make it easy, and explain how to use it. As usual, I encourage you to reduce mistakes by writing out Every. Single. Step. And do nothing in your head!

This video appears on the page: Factoring

Factoring by U (aka Z) Substitution

When the exponents get big, it's time to substitute. You'll need this to factor things like x4-16, x8-64, or x4+4x2-5.  Check with your teacher to find out how rigorous you have to be for full credit!

This video appears on the page: Factoring