WEBVTT
1
00:00:00.240 --> 00:00:02.649 A:middle L:90%
So in this example, we're being asked to salt
2
00:00:02.649 --> 00:00:04.969 A:middle L:90%
to given inequality. And then we're going to graft
3
00:00:04.969 --> 00:00:07.139 A:middle L:90%
the solution set on a number one. Well,
4
00:00:07.139 --> 00:00:10.019 A:middle L:90%
remember, solving inequalities is just like solving equations.
5
00:00:10.029 --> 00:00:11.769 A:middle L:90%
So the first thing we need to do is isolate
6
00:00:11.769 --> 00:00:13.769 A:middle L:90%
are variable. So the move, the three to
7
00:00:13.769 --> 00:00:15.820 A:middle L:90%
the right hand side of our inequality. We're going
8
00:00:15.820 --> 00:00:18.829 A:middle L:90%
to subtract three from both sides because three minus three
9
00:00:18.829 --> 00:00:21.559 A:middle L:90%
is zero. So these terms cancel out. So
10
00:00:21.559 --> 00:00:24.989 A:middle L:90%
now we're left with X is less than while negative
11
00:00:24.989 --> 00:00:28.800 A:middle L:90%
eight minus three is negative a weapon. So now
12
00:00:28.800 --> 00:00:31.399 A:middle L:90%
we've solved our inequality. So what we found is
13
00:00:31.399 --> 00:00:34.530 A:middle L:90%
that X is any number that's less than negative 11
14
00:00:34.539 --> 00:00:37.670 A:middle L:90%
. But remember, not equal to negative 11 now
15
00:00:37.670 --> 00:00:39.219 A:middle L:90%
, the second thing they want us to dio is
16
00:00:39.219 --> 00:00:40.929 A:middle L:90%
graft, a solution set on the number line.
17
00:00:41.320 --> 00:00:43.380 A:middle L:90%
Now, the one thing that you typically do when
18
00:00:43.380 --> 00:00:45.469 A:middle L:90%
you set up a number line is usually put zero
19
00:00:45.469 --> 00:00:47.200 A:middle L:90%
in the middle and you put tick marks up until
20
00:00:47.200 --> 00:00:49.399 A:middle L:90%
you get to the numbers you need. But you'll
21
00:00:49.399 --> 00:00:52.390 A:middle L:90%
find sometimes we might have answers that air really big
22
00:00:52.390 --> 00:00:54.700 A:middle L:90%
, like maybe the answer is 200. You certainly
23
00:00:54.700 --> 00:00:56.700 A:middle L:90%
wouldn't want to make a number line that that's large
24
00:00:56.710 --> 00:00:58.979 A:middle L:90%
, that large. So here's what you need to
25
00:00:58.979 --> 00:01:00.969 A:middle L:90%
dio You can just set up your number line.
26
00:01:02.509 --> 00:01:04.310 A:middle L:90%
The important number that you need here is our critical
27
00:01:04.310 --> 00:01:07.489 A:middle L:90%
number, which is negative. 11. So I'm
28
00:01:07.489 --> 00:01:08.590 A:middle L:90%
gonna put a tick mark in the middle and label
29
00:01:08.590 --> 00:01:11.900 A:middle L:90%
it negative 11. And what it implies is that
30
00:01:11.909 --> 00:01:15.129 A:middle L:90%
any value to the left of it is less than
31
00:01:15.269 --> 00:01:15.980 A:middle L:90%
, and any value to the right of it is
32
00:01:15.980 --> 00:01:19.430 A:middle L:90%
greater than which is exactly what a regular number line
33
00:01:19.430 --> 00:01:22.469 A:middle L:90%
means. Now some people will put in the values
34
00:01:22.939 --> 00:01:25.709 A:middle L:90%
just greater than just lesson, which is perfectly fine
35
00:01:25.709 --> 00:01:27.189 A:middle L:90%
. But you don't have thio. So remember to
36
00:01:27.189 --> 00:01:30.290 A:middle L:90%
graph X is less than negative 11 on the number
37
00:01:30.290 --> 00:01:32.230 A:middle L:90%
line. The first thing we need to figure out
38
00:01:32.239 --> 00:01:34.349 A:middle L:90%
is, should this be an open or close circle
39
00:01:34.939 --> 00:01:37.519 A:middle L:90%
? Well, because negative 11 is not a solution
40
00:01:37.530 --> 00:01:38.459 A:middle L:90%
. That means we should have an open circle.
41
00:01:38.469 --> 00:01:41.750 A:middle L:90%
So we're gonna have a open circle at negative 11
42
00:01:42.840 --> 00:01:44.819 A:middle L:90%
. And because our values of X have to be
43
00:01:44.819 --> 00:01:47.120 A:middle L:90%
less than negative 11, our values that would be
44
00:01:47.120 --> 00:01:49.250 A:middle L:90%
less than negative 11 would happen to the left of
45
00:01:49.250 --> 00:01:51.310 A:middle L:90%
negative 11. So on our number line, we're
46
00:01:51.310 --> 00:01:53.049 A:middle L:90%
going to shade in the left hand side of our
47
00:01:53.049 --> 00:01:57.420 A:middle L:90%
number line and now we have graft. A solution
48
00:01:57.420 --> 00:02:00.250 A:middle L:90%
set to represent X is less than negative 11.