00:00Find the set of x values that satisfy the equation absolute value of x minus 1 multiplied by absolute value of x plus 3 equals x minus 1.
00:06Find it.
00:06So, friends, what have we been given?
00:08The absolute value of x minus 1 multiplied by the absolute value of x plus 3 equals x minus 1.
00:14Now I know, friends, what should the product of two absolute value expressions be?
00:18It should be greater than or equal to 0.
00:21First, we need to address this issue.
00:24If x minus 1 is greater than or equal to 0, what happens if we move minus 1 to this side?
00:30Our x will be greater than or equal to 1.
00:33What does x greater than or equal to 1 mean, guys?
00:37x greater than 1 or x equal to 1.
00:40If you recall, we also covered in our logic lesson on inequalities and such expressions.
00:47So now, when we look at this, friends, I'm back to this expression again.
00:51Now, if x equals 1, what is 1 minus 1?
00:58It's zero, right?
00:59Multiplying 1 plus 3 equals 4.
01:03That equals 1 minus 1.
01:05Is equality being ensured, friends?
01:07It is being provided.
01:08They both come out as zero.
01:09So what are we going to do with x equals 1, guys?
01:12We can have it.
01:13Now let's look at it for x greater than 1.
01:18If x equals 1, then x is greater than 1.
01:21For x greater than 1, how do we get x minus 1 out of the equation?
01:27Of course, how does it come out as x minus 1, right guys?
01:32We'll take it out exactly as it is.
01:33For x greater than 1, how do we get x plus 3?
01:38Since it's positive, it comes out as x plus 3.
01:44And that was x minus 1.
01:47So, what if I move x minus 1 to this side?
01:51Don't simplify x minus 1 directly here.
01:54That's wrong.
01:56x minus 1 times x plus 3 minus x minus 1, which side should I move it to?
02:03x minus 1 equals 0.
02:05If I factor out x minus 1 on both sides, what do we have left here, x plus 3?
02:13Minus 1.
02:15That's equal to 0.
02:16What can we expect from this, guys?
02:17Either x equals 1, which we already have, but since x is greater than 1 here, in this part...
02:22We don't buy it.
02:23Or what are friends?
02:27Here's x plus 2.
02:30This could also be 0, right?
02:32Look, 0 or x plus 2 equals 0.
02:35So what is that?
02:35x equals x².
02:37From this, we get the square root of x².
02:39Okay, x came out as 2, but we had specified the condition that x is greater than 1.
02:43So what is this, guys?
02:44No roots will grow from here.
02:46So what happens then, guys?
02:48Our solution set contains only 1.
02:53sobrek 즉 kimme.
02:54Comence
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