This channel will contain video math lessons for some of the courses that I teach. Currently there are all the Trigonometry videos posted. I am currently beginning to work on AP Calculus AB videos. And, hopefully coming soon will be the videos for my College Algebra course.
On occasion, you may also find videos pertaining to my cross country and track teams as well.
I had this thought as well, and assuming it's somehow not always valid, I would think it's the better way to go. Especially when facing multiple different absolute values, I would think it's wise to resolve abs(x-3) as variably +/-(x-3).
i’m a freshman this year and this helps so much, i can’t focus on the textbook and it takes an hour to read the whole chapter, thank you so much i wouldn’t be able to do this class without your help.
There are also restrictions of the values for x. Set the absolute value to 0 x + 3 = 0 x = -3 This is the x intercept, and it determines which parts are reflected to a point. If we visualise this, we can see that this linear equation has a positive slope, and therefore the left side of the graph needs to have all of it’s negative y values reflected This can be written in piecewise notation: y = {x + 3, x >= -3} {-(x + 3), x < -3} The first part is where both the parent and the absolute value graph are the same, and the second part is where the part of the graph is flipped (the absolute value part). Solve for the original equation: x + 3 = 9 x = 6 Check if it satisfies the restriction x >= -3? 6 >= -3? True. 6 is a solution Do the same for the other equation. You’ll see that x = -12 satisfies the restriction of x < -3
For example, the equation |x - 1| = -1 has no real solution. We’ll solve both cases (x - 1) = -1, x = 0 -(x - 1) = -1, x = 2 If we substitute either x values into the equation, those answers are wrong, because they didn’t satisfy the restriction of x - 1 = 0, x = 1 Parent equation restriction: x - 1 = -1, x >= 1. Absolute value equation restriction: -(x - 1) = -1, x < 1 Neither answer is right because they didn’t satisfy the restriction. (while an absolute value can’t equal a negative number, I used it for the sake of this example and explanation)
The problem is you are assuming the expression in the absolute function to be only positive when you do that. However, it could also be negative and as a result, you lose -12 as an answer by distributing 4 and disregarding the absolute value. You can however use a similar approach by assuming the expression in the absolute value to also be negative: 4(-x-3) = 36 -4x-12 = 36 -4x = 48 x = -12 Just remember that there are possibly two answer when it comes to absolute values.
Wait, shouldn’t it be -228? 3:14 mark Ah, just saw the correction Love these videos btw, I’m no good at math but these videos really help me review a lot
if you need this for your job you should be getting a special class for it, instead of having it shoved into everyone's business making them more stressed.
Why aren't your video views increasing? And not reaching people? The reason is: 1. Your video is not being SEO properly 2. Your video is not reaching the right people 3. Not using video hash tags properly 4. Not sharing the video on social media There are a few more reasons. That's why your videos are limited to your channel. Can't get out In a word, your video is awesome. Such videos are in great demand. If you do these things correctly. Hopefully, you will get a lot of visitors. Feel free to ask me any questions.
Maybe a better way to teach this would be to graph this with an XY grid. Show, (2,1) then explain it's the midpoint of a line. Show point C and infer the other half of line. These are wonderful videos
Lots of people including me for A level Math. it’s saves lots of time. suppose you’re given A & B all 3x3 to show that (AB)^-1 = A^-1B^-1. I’m not gonna try to act genius 😂 at the end of the day all we need is to pass just show the process and punch those numbers in😂 no messing around.
@@WakefulR oh yeah I forgot ap math was the beginner level. Since we don't use terms like that here it all gets a bit confusing. Here linear algebra is a course all engineers, physisists and mathematicians have to take. It would be after you finish your first course in mathematics on a university level (Mathematical analysis of one variable) and calculators were not allowed during those exams. Calculators are usually only allowed when the important part of the exam isn't being able to do math, it's being able to understand the equations and which situation they might be used in. Like thermal-fluid sciences.
