00:00Now, let's talk a little about absolute, unique, and simple things.
00:04So, friends, what is absolute value, simple uniqueness?
00:07Now, when we are given an absolute uniqueness, our task is to convert that to a normal range, folks.
00:13Let's take a look at this.
00:14Let's start with our first scenario, friends. Let's say we have a number A.
00:18I'm saying that our number A is A greater than or equal to zero, friends.
00:23In this case, for example, if the absolute value of X is less than or equal to A.
00:34In this case, how do we write this as a unique interval, guys?
00:38The expression we're referring to as X will take the closed interval between A and -A, that is, between A and -A.
00:48We can write it as -A less than or equals X less than or equals A, folks.
00:53We can also show this on our number line, friends.
00:59I'm talking about real numbers.
01:02Let zero be in the middle, as the point of reference, which it is here.
01:08Isn't that minus A, guys?
01:11Its point of perfect symmetry with respect to zero is minus A.
01:13So, the distance from A to zero, which we call X, is minus A, right?
01:23So, our X is the set of points between -A and A, folks.
01:31Let's give an example.
01:39I'm just making it up, for example.
01:40For example, let's say 2 times X plus 3 is less than 7.
01:48This inequality
01:55Let's say it provides.
01:58Let's say X is a negative integer. What is the product of X and its integer values?
02:19So, when we look at our inequality, what is it, my friends?
02:232 times X plus 3 is less than 7.
02:27In this case, what is the range of these 2X plus 3, folks?
02:33If your friends say equals, you will take the equals sign.
02:36If it says less than or equal to, then sorry.
02:37If there is no equality, you will receive it in a way that avoids equality.
02:41So, for example, here it says "less than 7", but here it says "equals".
02:43That's why we chose A.
02:45We said less than or equal to.
02:47Here it is less than 7.
02:49It needs to be in the -7 range.
02:51The expression we call 2X plus 3, folks.
02:54So, in this case, we will now find the ranges of values for X.
02:59And these will be negative integer values.
03:01As soon as I looked
03:02-7 is less.
03:042 times X plus 3 is less than 7.
03:08What are we going to do, guys?
03:09We'll get 3 out of each side first, right?
03:11Or we'll add -3.
03:12I'm saying minus 3.
03:14I'm saying minus 3.
03:15I'm saying minus 3.
03:16Minus 10 is less than...
03:182 times X is less than...
03:20Because minus 3 canceled out plus 3.
03:22From there, 7 minus 3 equals 4.
03:24I'm dividing it in half from all sides.
03:26From where?
03:27Or we could say we multiply by 1/2.
03:29We believe this is more accurate.
03:30So what happens then, guys?
03:32X is left alone.
03:33It took away -2.
03:36This point is minus 5 less.
03:39Isn't that X, guys?
03:41It is less than 2.
03:43So, he'll take our X.
03:48integer values
03:50And what are your friends saying?
03:52Negative integer values.
03:54It could be minus 4.
03:56It could be -3.
03:57It could be minus 2.
03:58It could be minus 1.
04:00And if it asked within its normal values
04:03If it said the product of all integer values
04:05What was going to happen, guys?
04:06We were going to take 0 and 1 as well.
04:08It would have been 0 then anyway.
04:10Because there is a 0 swallow separation.
04:110 would encompass them all.
04:13Let's look at the product of these now.
04:15Since these are our values.
04:16Minus 4 times,
04:18minus 3 times,
04:19minus 2 times,
04:20minus 1.
04:21Now, these four statements
04:23Because it's a negative multiplication
04:24It will be a plus, friends.
04:25Plus 24.
04:28This is our answer.
04:30Now the second
04:32Let's look at our rule, guys.
04:35What we need to know here is...
04:37the absolute value of our x
04:39If greater than or equal to a.
04:44What do we do in this situation?
04:46Here are the friends
04:47Our x is either greater than or equal to a.
04:49or
04:51Our x is less than or equal to,
04:54It is minus a.
04:55Guys, these are the results.
04:57The results of some evidence.
04:59x is greater than or equal to a
05:00or x less than or equal to,
05:02It is minus a.
05:02We can write it like this.
05:04As inequality.
05:06As of December.
05:07Now, on the number line...
05:08If I want to show it.
05:12Based on 0
05:15minus a
05:18Here is our x
05:19Friends
05:20received
05:21intervals
05:22here.
05:26If the absolute value is x
05:27if greater than or equal to a
05:28x from here onwards
05:29from a
05:30What's up, guys?
05:31Great and equal.
05:33From minus a
05:34Small
05:35And
05:36equally
05:37We can get it.
05:39After knowing this as well...
05:40Examples related to these
05:41We will solve plenty of them, God willing.
05:44For example
05:45I'd like to give one away.
05:46A simple example.
05:482 times x
05:50But it happened.
05:51Anyway.
05:51Minus 5
05:55Let's make it greater than 7, folks.
05:58This inequality
06:04Let's ask the solution sphere about this as well.
06:08Now, when this happens, friends
06:092 times x minus 5
06:11is greater than 7
06:12What was it, guys?
06:13first
06:14or 2 times x
06:15minus 5
06:16It should be greater than 7.
06:18or
06:19second
06:202 times x
06:21minus 5
06:22is small
06:22It should be minus 7, folks.
06:25What happens in this situation?
06:26Friends from over there
06:27our x
06:28our x
06:28y times x
06:30is great
06:31That makes 12.
06:32from here
06:32What's coming, guys?
06:33x is greater than 6
06:36or
06:36secondly,
06:38We'll throw -5 over to this side.
06:39It becomes plus 5.
06:40Minus 7
06:41plus 5
06:41minus 2
06:42Divide by 2
06:43minus 1
06:43x
06:44is small
06:46minus 1
06:47or
06:48x is greater than 6
06:49values we mentioned
06:50our solution set
06:51It forms our range.
06:53So let's say
06:56our solution set
06:58If we write it like this
07:01negative infinity
07:03from the open range
07:04Friends
07:05minus 1
07:06why?
07:07Open range
07:08combination
07:10this in intervals
07:11if we write
07:12From 6
07:13big
07:14not equal
07:15Greater than 6
07:16And
07:17plus infinity
07:18That is our range.
07:20A little more
07:21if we write
07:22this in another way
07:23We can write more.
07:24solution set
07:25Let's do this a little bit
07:26Let's push it
07:27numbers of the whole
07:28difference
07:31in a closed range
07:32minus 1
07:346
07:34closed range
07:36we say.
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