00:00Absolute value x plus absolute value minus 2 times x plus absolute value 3 times x plus absolute
00:07The value minus 4 multiplied by x equals 10.
00:09Given this information, the question asks for the set of possible values of x.
00:13Now, when I look at it, I'm writing down the absolute value of x.
00:16Furthermore, I'm saying that we know that expressions in a multiplication situation, expressions in an absolute multiplication situation, can be written separately within the absolute value.
00:27isn't it?
00:27So, for example, here's minus 2 times x in absolute value, I'm writing this in absolute value as minus 2.
00:37I can write it as multiplied by the absolute value of x, right guys?
00:41Yes, in this case, when I write it like this, minus 2 times the absolute value, this absolute value, x plus all of it like this.
00:51I need to write, guys.
00:52Absolute value of 3 times absolute value of x plus absolute value of x plus absolute value of -4
00:59Multiplying the absolute value of x equals it.
01:03Now, let's think about this, friends.
01:05Here, let's factor out the absolute value of x, or let's do it like this.
01:08I'm writing the absolute value of x.
01:09Now, how do we derive absolute values of minus 2, guys?
01:12It comes out as 2, right?
01:13It will come back to you as a negative.
01:15Negative expressions.
01:16So the positives come out exactly the same.
01:18What was the point of absolute value anyway, guys?
01:20To be positive.
01:21In this case, I write it as plus 2 times the absolute value of x.
01:25Since I don't know the range of the absolute value of x, I can't deduce whether it's positive or negative right now.
01:30The equation is in my system equation.
01:33I'm saying plus, 3 times the absolute value of x plus or minus 4, which comes out as 4 with a minus sign in front.
01:39It's multiplied by minus 1, and the absolute value comes out as 4.
01:434 times the absolute value of x equals 4.
01:46Let's think about this now.
01:47What does the absolute value of x become if you add one support 'a', then 2a', and so on?
01:503 a.
01:503 a's plus 6 a's, 4 a's plus 10 a's.
01:53Then I say 10 times the absolute value of x.
01:58That's equal to 10.
02:00Step by step.
02:01I divide each side by 10.
02:02To find the absolute value of x.
02:04More precisely, to find x.
02:05I'll leave x alone.
02:07When I divide by 10, they cancel out.
02:10The absolute value of x is equal to 1.
02:12So what does this mean, guys?
02:14If the absolute value of x inside is 1 outside, then either the inside is 1 or...
02:23Secondly, friends, it's minus 1, so that when multiplied by minus 1, it comes out as 1, which is positive.
02:30So, what are the values I can acquire, folks?
02:34The possible values for x are -1 and 1.
02:38So, our answer is Ceyhan.
02:40Minus 1 and 1.
02:41Thank you for watching.
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