Master Absolute Value Equations in 5 Minutes SAT ACT Hacks You NEED to Know

All right. So, welcome to my YouTube channel. am the math test prep pro. And today, one of the things I'm going to go over for, standardized testing preparation is that, we're going to look at absolute value, absolute values of numbers and also of equations. And we're just going to kind of solve few just to see to give you feel of where where you're able to. All right. All right. So, if you look at the top, there's absolute value rule up there. It says absolute value of xals is the same as xals or x= negative So, basically, it's saying that if you take what's inside the absolute value and you set it equal to the positive and negative value of what's on the right hand side of that equal sign, then what we can do is just solve it from there. All right. So if we look at this one right here, the absolute value of Now remember if you find the absolute value of number like say the absolute value of six is six. Absolute value of -6 is six and then and so on and so on. So absolute value of -12 is 12. Absolute value of 12 is 12. So it's going to be the positive value of that number. So when you look at it and you apply it to the rule at the top posals is such that x= or x= negative you can just go ahead and solve it. So it's going to be = 6 or = -6. Right? Let's put that answer up there. So is it true? So it's always it's always good idea in math just kind of go through and check your work. so for here, if you plugged in six for the positive, excuse me, the absolute value of six equals 6. So that's true. Now for negative -6, if you plug that in for so the absolute value of -6= 6. That's also true. So the answer is correct. x= 6 or -6. So let's scoot this up. Let's look at number two. Scoot it up little bit more. All right. All right. So, what we have here is now we have an equation and it says the absolute value of + 4 = 9. So, we're going to use the same format. what I'm going to do is I'm going to write an equation where + 4 = 9 and solve. And also an equation where + 4=9 and solve. And that should give us our two x's. All right. So, let's look at it. So, + 4 = 9. That's the first equation. The other equation is + 9 or excuse me, + 4. Sorry about that, guys. That's not confusing. + 4 = -9. All right. So, I'm going to work on the left equation first. The left equation, have + 4 = 9. So, to get the by itself, I'm going to minus four from both sides. So, the comes down. What do we do to one side of the equation? We got to do to the other. So we have the -4 on the left, -4 on the right. So +4 and4 cancel out. The comes down. 9 - 4 is 5. Okay. So let's go over here. + 4 equals 9. So I'm going to do the same thing. I'm going to minus four on this side. Minus four on this side. These cancel out on the left hand side leaving me Over here have -9 - 4. So essentially what it is is it's -9 minus 4 and you can do the zip zip method zip zip right so it's9 +4 which gives you -3. All right so the answer x= 5 or x= -13. All right so in that problem let's let's check it. Let's do some brain checks. So if you plug in five for 5 + 4 is nine. Absolute value of 9 is nine. So that's correct. All right. So, -3 + 4 is going to give you -9. Absolute value of negative9 is nine. So, that checks out. All right. So, if you if you notice the pattern here, that's just our problem solving method. When we we see these types of equations on tests, we're going to take the absolute value and and set it equivalent to the positive and the negative value of what's to the right of the equation. All right. So here we have positive value of - 5 = 3. We're going to do the same thing, same method. - 5 = 3. Set it equal to the positive value. Then also set it equal to the negative value. And so what do we do from here? We solve. So on the left hand side of this equation, - 5. So to get rid of the five, I'm going to plus five. add those out. So these two cancel out leaving on the left side, 3 + 5, eight on the right side. All right, over here we have - 5 = -3. All right, so x5. Okay, so I'm going to do the same thing. Plus five on the left, plus five on the right to balance out the equation. These cancel out, leaving an over here equals two. Sorry, my math's little rusty. So equals 8 or two. And I'm do some brain math over here. I'm going to say, all right, I'm going to plug in this eight over here for 8 - 5 is three. Absolute value of three is three. So it checks out. The number two, two, plug that in for 2 - 5 is -3. Absolute value of -3 is three. So yeah, that works. 3 equals 3. Okay, let's go to the next problem. sec that straight. So the absolute value of equals 2. So this is kind of like the problem we started with. These are the simpler problems more straightforward problems. so absolute value of equals 2. So we got to use the rule that we started with x= 8 and x=8. So we're going to say all right = 2 that's the positive value also = -2 so there's no solving here that's just that's just the answer 2 -2 and we can even do little bit of mental math here and plug it in too right so for two we plug it in the absolute value of two is two so two equals 2 checks out there also plug in -2 the absolute value of -2 is two so it checks out so those both of those answers are All right. So, x= 2 or -2. All right. So, the last one, this is where we have to check our answers to make sure we don't have no curve balls. So, we're going to follow the format. So, the problem is is that the absolute value of - 2= -4. So, we're going to do is we're going to set it equal to the negative and positive values. - 2 = -4. Then also another equation over here. - 2 = 4. Let's do some math. Plug in and check just like we did in the previous problems. All right. so what do over here for for the left side, do for the right side. So to get rid of that two, I'm going to add two, right? So plus 2 cancels out leaving on the left hand side. -4 + 2 is -2. So I'm going come over here to this equation. - 2 = 4. So I'm going to do the same thing. Add two to each side. Plus two. = 6. So we got two answers. We got x= -2 and x= 6. So we want to plug them in and just see if it's true. So let's plug in -2 over here. Do some mental math. So -2 if you plug in -2 here. So it's -2 minus 2 absolute value equals -4. Right? So I'm just plugging in that -2 over here. Just zip zip. Right? So it's absolute value of -4als4. And that's not true because this equation comes out to 4= -4. So what that tells us is that -2 cannot be an answer. That is not value for in that equation. So let's plug in six. plug in six. So it's going to be 6 - 2 absolute value =4. Right? So plug them in. 6 - 2 is 4 =4. So absolute value of four is four. It does not equal4. Right? So that does not make sense, right? So none of these answers are correct. And usually when you see that, if you see the absolute value of - 2 equals a4, when you have an absolute value over here on the left and you have negative answer over there, it's usually undefined, right? There's no answer for that equation. So if you have any questions, let me know. If there's any problems that you want me to work on on my channel, I'd be glad to take requests. Just put it in the comments section. once again, this is the Math Test Prep Pro. really enjoy doing math, so you guys can see these videos and hope they're really helpful. So, if you could just please like and subscribe on my channel. But other than that, have good night. Thank you.