1
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Solve for x. And we have 5x plus 7 is greater than 3 times x plus 1.

2
00:00:09,228 --> 00:00:12,632
So let's just try to isolate "x" on one side of this inequality.

3
00:00:12,632 --> 00:00:15,733
But before we do that, let's just simplify this righthand side.

4
00:00:15,733 --> 00:00:20,333
so we get 5x plus 7 is greater than -

5
00:00:20,333 --> 00:00:27,533
let's distribute this 3. So 3 times x plus 1 is the same thing as 3 times x plus 3 times 1

6
00:00:27,548 --> 00:00:32,554
so it's going to be 3x plus 3 times 1 is 3.

7
00:00:32,554 --> 00:00:35,231
Now if we want to put our x's on the lefthand side,

8
00:00:35,231 --> 00:00:37,802
we can subtract 3x from both sides.

9
00:00:37,802 --> 00:00:40,282
That will get rid of this 3x on the righthand side.

10
00:00:40,282 --> 00:00:44,718
So let's do that. Let's subtract 3x from both sides, and

11
00:00:44,718 --> 00:00:51,759
we get on the lefthand side: 5x minus 3x is 2x plus 7

12
00:00:52,036 --> 00:00:55,933
is greater than - 3x minus 3x - those cancel out.

13
00:00:55,933 --> 00:00:59,383
That was the whole point behind subtracting 3x from both sides -

14
00:00:59,383 --> 00:01:05,867
is greater than 3. Is greater than 3. No we can subtract 7 from both sides

15
00:01:05,867 --> 00:01:08,267
to get rid of this positive 7 right over here.

16
00:01:08,267 --> 00:01:14,129
So, let's subtract, let's subtract 7 from both sides. And we get on the lefthand side...

17
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2x plus 7 minus 7 is just 2x. Is greater than 3 minus 7 which is negative 4.

18
00:01:24,080 --> 00:01:27,282
And then let's see, we have 2x is greater than negative 4.

19
00:01:27,282 --> 00:01:31,210
If we just want an x over here, we can just divide both sides by 2.

20
00:01:31,210 --> 00:01:36,223
Since 2 is a positive number, we don't have to swap the inequality.

21
00:01:36,223 --> 00:01:46,733
So let's just divide both sides by 2, and we get x is greater than negative 4 divide by 2 is negative 2.

22
00:01:46,733 --> 00:01:51,425
So the solution will look like this. Draw the number line.

23
00:01:51,610 --> 00:01:56,195
I can draw a straighter number line than that. There we go. Still not that great,

24
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but it will serve our purposes.

25
00:01:58,508 --> 00:02:05,133
Let's say that's -3, -2, -1, 0, 1, 2, 3.

26
00:02:05,133 --> 00:02:09,662
X is greater than negative 2. It does not include negative 2.

27
00:02:09,662 --> 00:02:14,367
It is not greater than or equal to negative 2, so we have to exclude negative 2.

28
00:02:14,367 --> 00:02:20,431
And we exclude negative 2 by drawing an open circle at negative 2, but all the values greater than that

29
00:02:20,431 --> 00:02:25,435
are valid x's that would solve, that would satisfy this inequality.

30
00:02:25,435 --> 00:02:29,985
So anything above it - anything above it will work.

31
00:02:29,985 --> 00:02:33,667
And let's just try, let's try just try something that should work.

32
00:02:33,667 --> 00:02:35,667
and then let's try something that shouldn't work.

33
00:02:35,667 --> 00:02:39,887
So 0 should work. It is greater than negative 2. It's right over here.

34
00:02:39,902 --> 00:02:48,834
So, let's verify that. 5 times 0 plus 7 should be greater than 3 times 0 plus 1.

35
00:02:48,834 --> 00:02:55,404
So this is 7 - 'cause this is just a 0 - 7 should be greater than 3.

36
00:02:55,404 --> 00:03:00,236
Right. 3 times 1. So 7 should be greater than 3, and it definitely is.

37
00:03:00,236 --> 00:03:04,400
Now let's try something that should not work. Let's try negative 3.

38
00:03:04,400 --> 00:03:10,831
So 5 times negative 3... 5 times negative 3 plus 7, let's see if it is greater than

39
00:03:10,831 --> 00:03:18,642
3 times negative 3 plus 1. So this is negative 15 plus 7 is negative 8

40
00:03:18,827 --> 00:03:21,569
That is negative 8.

41
00:03:21,569 --> 00:03:27,667
Let's see if that is greater than negative 3 plus 1 is negative 2 times 3 is negative 6.

42
00:03:27,667 --> 00:03:34,200
Negative 8 is not - is not greater than negative 6. Negative 8 is more negative than negative 6.

43
00:03:34,200 --> 00:03:39,769
It's less than. So, it is good that negative 3 didn't work 'cause we didn't include that in our solution

44
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set.

45
00:03:40,400 --> 00:03:43,399
So we tried something that is in our solution set and it did work.

46
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And something that is not, and it didn't work.

47
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So we are feeling pretty good.