Up next in 10
In the second part of our lecture on compound inequalities, we'll discuss how to solve absolute value compound inequalities.
Chapters:
00:00 Introduction
00:36 "Less Than" Compound Absolute Value Inequalities
02:30 " More Than" Compound Absolute Value Inequalities
03:10 Working on Examples
05:03 Multi Step Absolute Value Inequalities
06:28 Conclusion
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0:01
all right so
0:04
basically
0:05
basically we're talking about absolute
0:08
value inequalities right yesterday we
0:11
talked about two days ago we talked
0:12
about what the compound inequalities
0:15
where we had to split them and I wanted
0:16
to conjoin these and the other one but I
0:19
figured it would not be a good idea to
0:21
do that together so I wanted to split
0:23
this right so now we're going to talk
0:25
about this but then what we're going to
0:27
do is this we're going to have two two
0:28
separate cases and then we going to go
0:31
to the multi-step absolute value so the
0:33
first case is when we use less than
0:37
right less than so less than so that
0:39
means I have here absolute value of x is
0:43
less than or equal to
0:45
5 so how do I solve this problem so we
0:49
talked about how absolute value is
0:51
actually the distance between the number
0:55
and the given center right in this case
0:57
the center is five so basically I'm
0:59
saying here that I want the distance
1:01
between X and five to be less than what
1:05
less than or equal to five right but
1:08
because it's absolute value you have to
1:10
go to the left and to the right because
1:13
we have two cases does that make sense
1:16
so far no yes who says no why does it
1:20
have
1:21
to because it's absolute value right is
1:25
actual value of x I don't know the value
1:27
of x x can be either what5 or or
1:30
negative so that can go either way so as
1:33
long as the distance is less than five
1:36
right so now I want you all to think
1:38
about what we talked about two days ago
1:40
right so if x is in between here what am
1:43
I referring to is that imply or or does
1:47
it imply
1:48
end end right because X is what in
1:52
between -5 and what five so therefore to
1:57
solve this problem I want my X to be
1:59
what
2:00
between and 5 that means I want the
2:03
distance between zero between um X and
2:07
this number to be five or less and the
2:09
only way that's going to happen if x is
2:12
in this spacing here does that make
2:15
sense right so this is how you deal with
2:18
this when this is less than we're going
2:19
to come up with a general case where
2:21
every time you have a less than you're
2:23
always going to end up with these
2:24
cases all right does that make sense now
2:28
we're going to move on to the more
2:30
right so more so in this case I want the
2:33
distance to be more than or equal to
2:34
what five so that means X has to be
2:38
where either
2:40
here or here does that make sense right
2:45
so in this case what is the key word is
2:47
it n or or or or so that's the only two
2:51
cases we have so this is why we needed
2:52
to do the other thing on on on Tuesday
2:55
so that we can build off of that right
2:57
so when you have that to solve it you're
3:00
going to have your two
3:03
cases does that make sense yes all right
3:07
so now let's take some example assume I
3:13
have um I won't do this yet cuz this is
3:16
a little tough right so assume I have
3:18
absolute value of x is less than 7 how
3:22
am I going to solve
3:27
this x is
3:30
and X is L that's right you can either
3:34
write this way or you can say x is more
3:37
than7 and X is less than 7 either one of
3:41
those will be fine you can just do it
3:42
this way and then just save yourself a
3:43
lot of trouble does that Mak sense are
3:46
we good now assume I change
3:51
it now I have absolute value of y is
3:55
greater than 20 how do I solve this
3:59
okay well how would you set this up now
4:02
abute value of y is more than 20 you'd
4:05
have mhm um Y is less
4:10
than y is less than uhuh less than
4:13
20 oh five 20 oh negative 20 or or Y is
4:20
less or greater than 20 20 does that
4:23
make sense that's all you need to worry
4:25
about right so once you have this just
4:28
know you always going to have the same
4:30
cases every time I know you guys love so
4:32
is this confusing or was I hyping it a
4:34
little too
4:35
much it's not confusing right no all
4:38
right good cuz last year when I did it
4:41
do you know I'm like whatever so so I
4:46
was thinking okay maybe you know maybe
4:47
you learn you go and you learn cuz I
4:49
guess maybe this is different maybe your
4:51
brains are a little bit more stand
4:58
there all now that we know that right so
5:01
how would you set this up it's the same
5:02
way how would you set this
5:04
up uh Jack knowing that how would you
5:09
set this up here it's the same
5:13
principle uh 6x - 5 is less than 13 and
5:18
then 6x - 5
5:23
is-3 that's it you see that's it and now
5:26
we can solve this right does that make
5:29
sense
5:31
um Gavin so what if I had 6x - 5 greater
5:36
than or equal to 13 how would you set
5:38
that up before you solve it
5:42
um you just do the same thing but the
5:44
sides so how would you do
5:52
it 6x - 5 oh if you do that's this year
5:57
remember when you have a less than it
5:59
implies
6:01
what a right we have a more than it
6:04
implies what or so we going to have what
6:07
6x - 5 is less than what -3 or 6x - 5 is
6:15
greater than 13 does that make sense so
6:19
if you can retain these if you can
6:22
retain this information and that you
6:25
will be fine right so let's just go
6:26
let's say if absolute value of x is less
6:28
than a in general X has to be between a
6:33
and a and if absolute value of x is more
6:36
than a then in general X has to be less
6:39
than a or X has to be more than a and
6:42
then you can go ahead and solve it yes
6:44
sir I'm just pointing out you put less
6:47
than instead of less than or equal to oh
6:49
yeah yeah thank you for cing
6:52
that he get oh on a second that's not
6:55
that's not an error that's just an
6:57
Omission that's an omission
7:04
no
7:06
G5 that's an Omission that's an
7:09
Omission that's Omission on accident you
7:13
omitted it by mistake yeah accident it
7:16
happens to every one of
7:22
us I never claim I was perfect he that
7:25
so you guys know what to do here right
7:28
so now this is what we're going to work
7:29
on so with that say I want to go to the
7:31
book and then work on some problems so
7:33
if you open your book and if you go on
7:35
page 43 right if you go on page 43
7:38
there's a table there that gives you how
7:40
to set it up if you if you forgot what I
7:42
said here you can go back to your book
7:44
on page 43 and there's a way to remember
7:47
that right now if I'm if I'm generous on
7:50
the test I might give you that right but
7:53
I don't know how I'm going to feel that
7:55
day page 43 if you look on page 43 at
7:59
the bottom you're going to see a table
8:00
that that tells you exactly how to set
8:02
them up
8:04
please at least LEL give us the forance
8:08
but the honor she wouldn't
8:11
give so at least all level
8:16
get
8:19
so I want you all to solve
8:22
this uh I'll
8:30
oh
8:44
no go ahead and solve these two all
8:47
right go ahead and solve these two