Learning Algebra MUST Know How to Solve Absolute Value

So, here is the equation, absolute value of + 3 is equal to 10. So, we're not going to start with this equation. We're going to do simpler version of this equation, right? And we're going to first make sure you understand what absolute value is. So, let's go down here and take look at this equation here. The absolute value of is equal to 10. Now, is what? Well, that's variable, right? But, it just represents some number. So, if asked you, "Hey, the absolute value of some number is 10, what is that number?" Okay? Well, hopefully you you would say, kind of what the what it is there, Mr. YouTube math man. it it's 10." Okay? Because absolute value of 10 is 10, right? So, that makes sense. And hopefully those of you out there who, you know, if you're you know, obviously watching this video, have basic understanding of absolute value. But, that's not the only number where we take the absolute value of of the particular number and get our 10 as the answer. We can also take the absolute value of -10 and our answer would be 10. Okay? So, this case, can either be 10 or -10, right? Because if we plug in 10 for or -10, we'll get 10 as our answer. Okay? So, we really have two answers to this basic absolute value equation. And this is kind of my first major concept that want to really emphasize is when you have an absolute value equation, all right? When you see an absolute value equation like this one here, you're going to have two solutions. You're always going to have two solutions for this very simple reason right here. in this little basic absolute value equation, we can come up with two different values and get the right answer. Now, why is that? Well, let's go ahead and talk about that right now. So, we just said that the absolute value of -10 is 10 and absolute value of 10 is also 10. But, why is that? Well, absolute value by definition is the distance number is from zero, okay? So, here's our little number line here. Here is 10 and here is -10. How far is 10 from zero? Well, if you had little tape measure or ruler, it would be 10 units away from zero, okay? Well, how far is -10 from zero? It's the same distance. Remember, we measure distance with positive value, okay, or displacement. So, from this distance from here to here is the same as here to here. So, distance is going to be measured in positive units, typically speaking. So, the distance from -10 to zero is the same distance as zero to 10, okay? That's why when we take the absolute value of number, you're really kind of asking that number, "Hey, how far are you from zero?" "Hey, -10, how far are you from zero?" "I'm 10 units." "Hey, 10, how are far are you from zero?" "I'm also 10 units away." Okay, so that's just quick rehash of absolute value. So, again, remember, there's always going to be two solutions to an absolute value equation. So, now I'm going to show you the actual steps to solve an absolute value equation. But, if you understand this part of this, you know, what I'm talking about here, the steps I'm going to show you here right now are going to make much more sense. You're going to be able to kind of connect the dots, if you will. Are you struggling in math because of confusing lessons? Maybe the teacher's not showing you all the steps you need or things are happening too fast. Well, there is better way. So, come on over to my math help program at tcmathacademy.com. There you'll find clear step-by-step instruction by me that will definitely make huge difference in your math success. So, make sure to check out all my courses by following the links in the description. Okay, so now that we understand these concepts about absolute value equations, we can kind of look at this scenario. We got the absolute value of + 3 is equal to 10. So, I'm looking at + 3 and I'm like, "You know what, + 3? know you're trying to disguise yourself. you are really 10 or -10. You must be, right? Cuz the absolute value whatever, it doesn't make difference what it is. If the answer is 10, the only way can get the absolute value of anything, just think of it like this. The absolute value is equal to 10, whatever you plug in in in here, we already talked about it, can only be two values. If you're going to get the answer of 10, it can either be 10 or -10. So, you're looking at + 3 and you're like, "Yes, see that you're trying to disguise yourself as either 10 or -10." So, + 3 must be equal to 10 or -10, right? And we already kind of talked about that. There's only two values that make this statement true, okay? If you're the result of taking the absolute value of number is 10, well, you can only get that way only get that result from -10 and 10. Okay, so what you're going to do when you're solving an absolute value equation is take what's inside the absolute value function and set it equal to both the positive and negative of this the value that we're looking to solve for, okay? So, + 3 in this case must be equal to 10 or -10, okay? So, instead of just memorizing this, now you understand why, right? You're like, "Okay, get this." And you'll understand, you know, kind of the underlying reasons. So, now we just have to solve these basic equations. + 3 is equal to 10. All we have to do here is subtract three from both sides of the equation. We get is equal to 7. Here, we'll subtract three from both sides of this equation and we get is equal to -13. And again, we have our two solutions to this absolute value equation. Okay? All right. So, if you understand this, then you're going to definitely now truly be certified professional expert in the area of solving absolute value equations. But, there are much more challenging absolute value equations. You can have things like this, 2X absolute value. Let me kind of write this little bit neater. So, what I'll just give you an example. Let's something like you have 1/2 absolute value of 2X - 3 absolute value + 7 is equal to, let's say, 16. Okay? So, in this particular case, we're going to do the same thing. But, before we do that, what we need to do is get the absolute value function all by itself on one side of the equation. And we need to get just one number on the other side. And then we're going to take the same steps. So, in this case, what you'll do is you'll subtract seven from both sides of the equation first. We do that, and then we'll go ahead and multiply both sides of the equation by two to clear this fraction out. What you never do when it comes to absolute value equations is use the distributor property. Okay? This is an absolute value function. Don't confuse this with parentheses. So, you know, this problem that we just solved here, this absolute value of + 3 is equal to 10, is basic problem. There are other things you need to kind of, you know, practice when it comes to solving absolute value equations to really kind of get that full certification professional expert in this area. Again, you know, in math, what you want to do is get great instructions to understand the concepts, all right? Break it down so you really do have comprehension. Then, what you want to do from that point forward is start to solve easy equations and build up your skill set. You have to practice, all right? This is no different than trying to learn any other skill. Let's suppose you're trying to get better at basketball, okay? Would you watch the TV all day, watch the NBA or college basketball, and be like, "Look at I'm watching all this TV, I'm watching all these professional basketball players, therefore my skills are going up." That's not the case, right? That is not the case at all. So, you watching me solving equation, that's great, and certainly appreciate it, but you're not going to develop those skills unless you practice, okay? Now, the same thing here, let's kind of talk about practice, right? Let's say, "Okay, I'm going to practice basketball. Here is my, you know, little hoop here. look at me, just made one basket. Now, let me shoot another one. made two baskets. Well, therefore, must make every single, you know, basket that attempt." Is that the case? No, right? So, just because you are able to solve one or two problems, you have to solve wide variety of problems. Remember, mathematics is collection of skills. You have to if it all depends how badly you want to learn math. There are no shortcuts, okay? But, if you kind of put in the work, all right, you'll be proud of the results. That can assure you, okay? Never, ever give up. No one listening to this video or watching this video is not smart enough, not capable enough to really go as far as you want in math. But, does require work and effort, and most importantly, it requires great math instruction. Okay, so if you need additional help with absolute value and there's other things about it. There's actually absolute value is big topic. There's absolute value inequalities, there's absolute graphing absolute value functions. So, we're talking about algebra. So, if you need additional help with this, do have lot more videos on absolute value on my YouTube channel, but you'll find absolute value, you know, full chapters of this stuff in my algebra courses. Again, you can check those out by following the links in the description. But with that being said, definitely wish you all the best in your mathematics adventures. Thank you for your time, and have great day.