00:00Since minus one is less than a is less than zero and b is less than the absolute value of b is less than b squared, inside the absolute value...
00:07The question asks us to find the equivalent of the expression a minus absolute value of a minus b plus absolute value of a minus 2b.
00:13Friends.
00:14Now we are given two inequality intervals, right guys?
00:18Yes.
00:18Now I know that I want to address b first.
00:22b less than absolute value b less than b squared.
00:27This is already given. Between minus one and zero is a.
00:32Okay guys, looking at this, can I find the range of 'b' within a number range?
00:36Yes, I can find it.
00:37Now I know, guys, that the feeling of x being greater than zero comes out as the absolute value of x, right?
00:45Friends?
00:46But when we look at it, it says b is less than the absolute value of b.
00:52We've already covered these topics, guys.
00:53If you don't have it memorized, here's what you should do.
00:57You can find the absolute value of b yourself.
01:00We can say that the absolute value of b is greater than b, right friends?
01:05That's why, friends.
01:10Alternatively, you'll easily know that 'b' is a negative number.
01:15Because its absolute value is greater than its actual value.
01:17B negative.
01:22You can also do this by opening it, guys.
01:24How do you open it?
01:25The cases where B is greater than zero, less than zero, or equal to zero.
01:29So, in the end, the absolute value of b is greater than b, folks.
01:33Therefore, b is negative.
01:35You are saying that B is missing something.
01:36Isn't the absolute value difference greater than the difference itself, my friends?
01:38Yes, now b is negative.
01:40Let's leave this aside.
01:41Since it's B negative, that's the situation, folks.
01:48B is smaller.
01:49The absolute value of b is less than...
01:52B squared, friends.
01:55Can I substitute -b for the absolute value of our B?
01:59It comes out as negative, right?
02:00Yes, I can write.
02:02B is smaller.
02:02Minus b is less than .
02:04B squared.
02:04Is it possible?
02:05It is possible.
02:05So what happens when this happens, guys?
02:08I divide each side by b.
02:09Remember, B is negative.
02:12So what happened in this situation, guys?
02:14Since B is a negative number, the direction of our inequality will change because we are dividing by b on both sides.
02:20What will happen in this situation?
02:23One is big.
02:24This is part one.
02:25This section is minus one.
02:28It's big.
02:29The square of B divided by b is b.
02:32As you can see, friends,
02:33Our b actually
02:36What is minus one, guys?
02:39That's a small number.
02:40Accordingly, friends,
02:45Our b being the smallest.
02:48I'm saying minus one is less than minus one, folks.
02:51When I combine this and that, I write about inequality in common.
02:55a is less than zero.
02:59So, folks, I can now move on to my question.
03:02I found this range.
03:03This is very important.
03:04Friends, when we look here,
03:05He said that in an absolute space, it's a minus b.
03:08Let's take a look at this.
03:09So, it was b less than a, right guys?
03:11We can find that place from here.
03:13We can write in some situations.
03:15In some cases, very large weights are involved.
03:16We don't implement it.
03:18Friends, what is a minus b?
03:20If we move b to the other side.
03:21Here, b is less than a.
03:23a minus b is greater than zero.
03:26Isn't it?
03:27So what are we going to do then?
03:28That part, that is, absolute value of a minus absolute value of a minus b.
03:36What are we going to do with this part, A minus B, guys?
03:39We'll take them straight outside.
03:40It will come out exactly as it is, right?
03:41It won't receive any negative marks or anything like that.
03:42So what happens to this place then, guys?
03:43In absolute terms, it comes out as a minus b.
03:53It's also equal to that.
03:54a minus a plus b becomes.
03:58The 'a's cancel each other out.
04:00The absolute value is b.
04:06The absolute value is b, folks.
04:08So, when we do that, friends, let's leave this place aside for now.
04:12What was our b anyway?
04:14It was less than minus one.
04:15The absolute value of b is also equal to... friends.
04:17Wouldn't it come out as -b?
04:19For a number less than b minus one.
04:21Yes.
04:21Now let's look at a minus two b.
04:24Let's leave this part aside for now.
04:27Our question also included a minus two b's.
04:33Friends, here, minus one is a smaller number.
04:36We have a range where a is less than zero.
04:38What is "b" and "ben", friends?
04:41I'll write it here.
04:42I know that our 'b' is also less than minus one.
04:45So, in order to achieve this,
04:47in order to obtain it as an inequality,
04:48What happens if I multiply both sides by minus two?
04:50It's right here.
04:52Minus two b,
04:53big kind of friends,
04:55That would be two, right?
04:57Yes.
04:58Minus two b,
05:00large species,
05:01two.
05:02I'm writing this down too, guys.
05:03I'm gathering them side by side.
05:05Minus one plus two equals one.
05:07So, the expression we call 'a minus twob' is actually a natural number greater than one.
05:12So, it's a number greater than one, folks.
05:15It was positive.
05:16Now that we know that, we can do it.
05:19There was minus b here.
05:20Right, guys?
05:24Plus, I say.
05:26I found this place too.
05:27The absolute value of a minus two b.
05:29And since it's a positive number, it goes straight out.
05:32A minus two b.
05:34Let's gather together, friends.
05:35Minus b.
05:36Minus two plus one b.
05:37Minus three thousand.
05:38We find our answer as A minus three b.
Yorumlar