1
00:00:00,610 --> 00:00:03,180
Solve for a and
check your solution.

2
00:00:03,180 --> 00:00:06,054
And we have a plus
5 is equal to 54.

3
00:00:06,054 --> 00:00:07,470
Now, all this is
saying is that we

4
00:00:07,470 --> 00:00:10,310
have some numbers,
some variable a.

5
00:00:10,310 --> 00:00:13,484
And if I add 5 to
it, I will get 54.

6
00:00:13,484 --> 00:00:15,400
And you might be able
to do this in your head.

7
00:00:15,400 --> 00:00:17,820
But we're going to do it a
little bit more systematically.

8
00:00:17,820 --> 00:00:19,570
Because that'll be
helpful for you when we

9
00:00:19,570 --> 00:00:21,070
do more complicated problems.

10
00:00:21,070 --> 00:00:23,361
So in general, whenever you
have an equation like this,

11
00:00:23,361 --> 00:00:24,930
we want to have the variable.

12
00:00:24,930 --> 00:00:29,670
We want this a all by itself
on one side of the equation.

13
00:00:29,670 --> 00:00:31,360
We want to isolate it.

14
00:00:31,360 --> 00:00:32,819
It's already on
the left-hand side,

15
00:00:32,819 --> 00:00:34,360
so let's try to get
rid of everything

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00:00:34,360 --> 00:00:35,490
else on the left-hand side.

17
00:00:35,490 --> 00:00:37,490
Well, the only other thing
on the left-hand side

18
00:00:37,490 --> 00:00:38,580
is this positive 5.

19
00:00:38,580 --> 00:00:42,440
Well, the best way to get rid
of a plus 5, or a positive 5,

20
00:00:42,440 --> 00:00:44,910
is to subtract 5.

21
00:00:44,910 --> 00:00:46,300
So let's subtract 5.

22
00:00:46,300 --> 00:00:50,110
But remember, this says
a plus 5 is equal to 54.

23
00:00:50,110 --> 00:00:52,180
If we want the
equality to still hold,

24
00:00:52,180 --> 00:00:54,430
anything we do to the left-hand
side of this equation,

25
00:00:54,430 --> 00:00:57,550
we have to do to the right
side of the equation.

26
00:00:57,550 --> 00:01:00,660
So we also have to
subtract 54 from the right.

27
00:01:00,660 --> 00:01:03,090
So we have a plus 5 minus 5.

28
00:01:03,090 --> 00:01:05,030
Well, that's just
going to be a plus 0.

29
00:01:05,030 --> 00:01:08,080
Because if you add 5 and you
subtract 5, they cancel out.

30
00:01:08,080 --> 00:01:10,400
So a plus 0 is just a.

31
00:01:10,400 --> 00:01:14,520
And then 54 minus 5, that is 49.

32
00:01:14,520 --> 00:01:15,220
And we're done.

33
00:01:15,220 --> 00:01:16,975
We have solved for a.

34
00:01:16,975 --> 00:01:19,460
A is equal to 49.

35
00:01:19,460 --> 00:01:20,810
And now we can check it.

36
00:01:20,810 --> 00:01:24,270
And we can check it by
just substituting 49 back

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for a in our original equation.

38
00:01:27,100 --> 00:01:29,600
So instead of writing a
plus 5 is equal to 54,

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let's see if 49 plus
5 is equal to 54.

40
00:01:32,040 --> 00:01:34,010
So we're just
substituting it back in.

41
00:01:34,010 --> 00:01:39,920
49, 49 plus-- let me do that
in that same shade of green.

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00:01:39,920 --> 00:01:43,730
49 plus 5 is equal to 54.

43
00:01:43,730 --> 00:01:45,270
We're trying to check this.

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49 plus 5 is 54.

45
00:01:48,210 --> 00:01:51,140
And that, indeed,
is equal to 54.

46
00:01:51,140 --> 00:01:54,080
So it all checks out.