1
00:00:00,760 --> 00:00:03,370
Solve for x and
check your solution.

2
00:00:03,370 --> 00:00:07,920
We have x divided
by 3 is equal to 14.

3
00:00:07,920 --> 00:00:11,320
So to solve for x, to figure
out what the variable x must

4
00:00:11,320 --> 00:00:14,135
be equal to, we really
just have to isolate it

5
00:00:14,135 --> 00:00:15,760
on the left-hand side
of this equation.

6
00:00:15,760 --> 00:00:16,884
It's already sitting there.

7
00:00:16,884 --> 00:00:19,490
We have x divided
by 3 is equal to 14.

8
00:00:19,490 --> 00:00:24,960
We could also write this
as 1/3 x is equal to 14.

9
00:00:24,960 --> 00:00:27,730
Obviously, x times 1/3
is going to be x/3.

10
00:00:27,730 --> 00:00:28,840
These are equivalent.

11
00:00:28,840 --> 00:00:31,800
So how can we just end up with
an x on the left-hand side

12
00:00:31,800 --> 00:00:33,107
of either of these equations?

13
00:00:33,107 --> 00:00:34,440
These are really the same thing.

14
00:00:34,440 --> 00:00:36,370
Or another way, how
can we just have a 1

15
00:00:36,370 --> 00:00:38,990
in front of the x, a 1x,
which is really just saying

16
00:00:38,990 --> 00:00:40,650
x over here?

17
00:00:40,650 --> 00:00:42,860
Well, I'm dividing
it by 3 right now.

18
00:00:42,860 --> 00:00:46,420
So if I were to multiply both
sides of this equation by 3,

19
00:00:46,420 --> 00:00:47,680
that would isolate the x.

20
00:00:47,680 --> 00:00:50,100
And the reason that would
work is if I multiply this

21
00:00:50,100 --> 00:00:54,140
by 3 over here, I'm multiplying
by 3 and dividing by 3.

22
00:00:54,140 --> 00:00:55,310
That's equivalent.

23
00:00:55,310 --> 00:00:57,720
That's equivalent to
multiplying or dividing by 1.

24
00:00:57,720 --> 00:00:58,995
These guys cancel out.

25
00:00:58,995 --> 00:01:00,870
Remember, if you do it
to the left-hand side,

26
00:01:00,870 --> 00:01:03,004
you also have to do it
to the right-hand side.

27
00:01:03,004 --> 00:01:04,879
And actually, I'll do
both of these equations

28
00:01:04,879 --> 00:01:06,545
at the same time,
because they're really

29
00:01:06,545 --> 00:01:08,470
the exact same equation.

30
00:01:08,470 --> 00:01:10,970
So what are we going to get
over here on the left-hand side?

31
00:01:10,970 --> 00:01:15,350
3 times anything divided by 3
is going to be that anything.

32
00:01:15,350 --> 00:01:17,580
We're just going to
have an x left over

33
00:01:17,580 --> 00:01:19,050
on the left-hand side.

34
00:01:19,050 --> 00:01:22,100
And on the right-hand
side, what's 14 times 3?

35
00:01:22,100 --> 00:01:27,770
3 times 10 is 30,
3 times 4 is 12.

36
00:01:27,770 --> 00:01:29,510
So it's going to be 42.

37
00:01:29,510 --> 00:01:31,550
So we get x is equal to 42.

38
00:01:31,550 --> 00:01:33,120
And the same thing
would happen here.

39
00:01:33,120 --> 00:01:36,250
3 times 1/3 is just 1.

40
00:01:36,250 --> 00:01:39,820
So you get 1x is equal to
14 times 3, which is 42.

41
00:01:39,820 --> 00:01:41,250
Now let's just check our answer.

42
00:01:41,250 --> 00:01:44,060
Let's substitute 42 into
our original equation.

43
00:01:44,060 --> 00:01:52,190
So we have 42 in place for
x over 3 is equal to 14.

44
00:01:52,190 --> 00:01:54,370
So what's 42 divided by 3?

45
00:01:54,370 --> 00:01:57,210
And we could do a little
bit of-- I guess we call it

46
00:01:57,210 --> 00:01:58,200
medium-long division.

47
00:01:58,200 --> 00:01:59,690
It's not really long division.

48
00:01:59,690 --> 00:02:01,210
3 into 4.

49
00:02:01,210 --> 00:02:02,580
3 goes into 4 one time.

50
00:02:02,580 --> 00:02:04,370
1 times 3 is 3.

51
00:02:04,370 --> 00:02:05,250
You subtract.

52
00:02:05,250 --> 00:02:07,100
4 minus 3 is 1.

53
00:02:07,100 --> 00:02:08,370
Bring down the 2.

54
00:02:08,370 --> 00:02:13,110
3 goes into 12 four times.

55
00:02:13,110 --> 00:02:14,710
3 goes into 42 14 times.

56
00:02:14,710 --> 00:02:19,230
So this right over
here simplifies to 14.

57
00:02:19,230 --> 00:02:22,640
And it all checks
out, so we're done.