00:00The question asks us to multiply the absolute value of y plus 1 plus the absolute value of y minus 2 equals 5 by the y values that satisfy this equation.
00:06I want to write to Kudu first.
00:08The absolute value of y plus 1 plus the absolute value of y minus 2 equals 5.
00:14Now, folks, get used to this.
00:17The value that zeros out inside the absolute value is the critical point.
00:20Critical point 1.
00:22If y plus 1 equals 0, then the value that makes the content zero is y equals -1.
00:30Why did I find this?
00:31We'll be examining their ranges, folks.
00:33Y equals minus 1.
00:35Critical point 2.
00:38That equals y minus 2.
00:40If Y minus 2 equals 0, then our y has two critical points here.
00:45So, looking at it from this perspective, it's like, what was it again, guys?
00:52I think it will be easier to understand from here when I create the symbolic representation.
00:56The "you two" part is also nice in this case.
00:58This is where things go, folks, plus infinity.
00:59Let's consider this as negative infinity, please.
01:02If we substitute 2 and -1 here, will the equation hold true?
01:07Minus 1.
01:08I'll buy them if he provides them.
01:10Minus 1 plus 1 0.
01:11Minus 1, minus 2, minus 3 comes out as 3.
01:14Is 3 equal to 5?
01:15No.
01:152.
01:152 plus 1 equals 3.
01:17If you subtract 2 from 2, how many is it?
01:180.
01:182 plus 1 made it 3.
01:20Does 3 equal 5?
01:21No, friends.
01:22So these places aren't suitable.
01:23I won't buy these.
01:24Points -1 and -2.
01:25We're already at a critical point.
01:27Okay, so when I look at it, it's for values greater than 2, friends.
01:30Those upper brackets are always the points that determine the root, or y.
01:34Our critical points.
01:35And below is the equation we were given, folks.
01:40So I'm not going to write absolute value of y plus 1 plus absolute value of y minus 2.
01:46Now, friends, how do you subtract y plus 1 for values greater than 2?
01:50Of course, the result will be positive, right guys?
01:53Y plus 1.
01:54I'm writing it directly.
01:55Y plus 1.
01:56For values greater than 2, add y plus 1.
01:58So it comes out directly as positive.
02:00How do you subtract 2 from 'plus'?
02:03So, if y is greater than 2, what is minus 2, guys?
02:06Y is greater than zero.
02:08So it provides it.
02:09Friends, this also comes out as positive when y is minus 2.
02:11That equals 5.
02:142 minus 1 equals 5, which equals 2.
02:19We move -1 to this side, plus 6.
02:22What can we deduce from this, friends?
02:23If we divide each side by 2.
02:25To leave Y alone, number 3.
02:26So, we said that y 3 is for values greater than 2.
02:31Does it provide that?
02:32It provides 3.
02:323 is a greater value than 2.
02:33We're going to get this, guys.
02:34So, this is a value that will be provided when we replace it.
02:37It's already visible when we place it.
02:38A simple example.
02:39When you look at the range between -1 and -2, friends...
02:42So, in the range from -1 to 2, what is y plus 1, guys?
02:48Of course, that's a positive value, isn't it?
02:51Y plus 1 goes straight out.
02:54I'm doing it quickly, guys.
02:55If Y is minus 2, let's take these as a fraction.
02:58Y is minus 2, folks.
02:59Minus 2 will be less than zero, folks.
03:01It will be minus y = minus 2.
03:05Will the y-value you just found provide it?
03:07Let's take a look at it.
03:08What does our Y stand for here?
03:10Between -1 and -2.
03:13I'll write these down too.
03:14Now the 'y's cancel each other out.
03:15I wrote zero times y.
03:18Right, guys?
03:20Plus 3.
03:23Is it equal to 5?
03:24Does 3 equal 5?
03:27No, it is not.
03:28Right, guys?
03:29In this case, we won't get any roots from here.
03:32So what are we going to do, guys?
03:34We'll skip this.
03:35What else is the solution here?
03:36Within this range, though.
03:38So what happens when y is less than -1, guys?
03:41Our Y plus 1 will of course be negative.
03:43Minus y minus 1.
03:45I'm writing it down right here too.
03:47I multiplied it by a negative number, guys.
03:49Because it's negative, it comes out from the absolute ground.
03:51I'm just saying it directly now because we need to be quick.
03:53Otherwise, we won't be able to cover all the topics.
03:55Minus y minus 1.
03:56The absolute value of y is plus or minus 2.
03:59Of course, this will come across as a negative statement, won't it, guys?
04:02He'll get a negative score.
04:03I'm writing it as minus y plus 2.
04:04That's equal to 5.
04:06Minus 2 plus 1 equals 5.
04:09Minus 2 equals 4.
04:11Our Y is equal.
04:13We find it here as -2.
04:14So what was this place for y minus 2?
04:17Our Y is lowercase.
04:18It is minus 1.
04:19Minus 2 is less than minus 1.
04:20You'll try it right away.
04:21Since minus 2 is less than minus 1, we also take this square root.
04:24What were my friends asking me?
04:25The question asked for the product of the Y values.
04:27What was your solution?
04:29Let's write that down first.
04:30It was between -2 and -3.
04:32In this case, the product is y1 times y2, which is equal.
04:36Minus 2 times 3 equals 3.
04:39It is minus 6.
04:39Our correct answer.
04:41The answer has been found, friends.
04:42Minus 3 minutes.
04:421 at -2.
Yorumlar