00:00Let x less than y less than 0 less than z. Then, the absolute value of z minus x minus the absolute value of x.
00:08plus y plus absolute value of y minus z
00:10The question is about equality, so I'm writing it here right away: x is smaller than y, y is smaller than zero, and y is smaller than z.
00:18Now, friends, if I look at the absolute value of z minus x, I'm processing these absolute values piece by piece, and that equals... outside of it.
00:24How will it come out?
00:25Okay friends, I know that x is less than z, right? Look, it's given here. So, friends, if I move x to this side...
00:35Or, if I subtract x from each side, which would be a more accurate expression...
00:39What is zero, friends? It's less than z minus x, meaning our z minus x is greater than zero. So we can directly take this outside.
00:47we can derive an expression greater than zero
00:49Let's leave z minus x out and see x plus y. We're not doing anything with what's given, friends, with the given data.
00:59Starting from there, we are moving towards our question.
01:02Pay attention to even the smallest detail, friends; even they want to tell you something. x plus y absolute value x plus
01:09Let's look at y now. I know that, friends...
01:12What is it? I'm doing it here, let me do it like this too: x is less than zero, y is also less than zero, right? That's what we're given, friends.
01:21If I move these side by side, what happens? x plus y becomes less than zero, right? What if x plus y is less than zero?
01:28what do you take with you when you leave?
01:29Let's take it out as a negative and make it positive, so think of it as multiplying by minus one. When we do that, friends, x plus the negative number in the parentheses.
01:36y
01:36That equals minus x minus y, in its output form. Now let's look at y minus z, its absolute value.
01:44inside
01:45And that equals, friends, y minus z like this:
01:50y is less than z, what is that anyway guys? Don't confuse the zero at all, y is less than z, so put z this way.
01:59If we throw it, friends
02:00What is y minus z? It's less than zero, right? Okay, so we put a minus sign in front of it and get minus y minus z.
02:08that is equal to
02:09What is it, friends? It's the exact opposite: z minus y.
02:13So, what did they tell us? They said to take z minus x. How do we get z minus x minus x plus y?
02:20It came out as minus x minus y.
02:23How did we get plus y minus z? Here, pay attention to the signs of z minus y, the order of operations, and the multiplication of the given numbers.
02:34Let's pay attention to sign multiplication, friends.
02:35I'm going step by step, z minus x, distributing the minus inside, plus x plus y plus z minus y, the y's are each other
02:45The x's cancel each other out, minus x plus x is zero, y minus y is zero, z plus z is equal to
02:52ki z'dir
02:52So, our answer is z, which means it's Ceyhan. 2 times z is our result.
02:57Our result is z.
02:57z'ini iz
02:57z'ini iz
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