0:00:00.760,0:00:03.370
Solve for x and[br]check your solution.

0:00:03.370,0:00:07.920
We have x divided[br]by 3 is equal to 14.

0:00:07.920,0:00:11.320
So to solve for x, to figure[br]out what the variable x must

0:00:11.320,0:00:14.135
be equal to, we really[br]just have to isolate it

0:00:14.135,0:00:15.760
on the left-hand side[br]of this equation.

0:00:15.760,0:00:16.884
It's already sitting there.

0:00:16.884,0:00:19.490
We have x divided[br]by 3 is equal to 14.

0:00:19.490,0:00:24.960
We could also write this[br]as 1/3 x is equal to 14.

0:00:24.960,0:00:27.730
Obviously, x times 1/3[br]is going to be x/3.

0:00:27.730,0:00:28.840
These are equivalent.

0:00:28.840,0:00:31.800
So how can we just end up with[br]an x on the left-hand side

0:00:31.800,0:00:33.107
of either of these equations?

0:00:33.107,0:00:34.440
These are really the same thing.

0:00:34.440,0:00:36.370
Or another way, how[br]can we just have a 1

0:00:36.370,0:00:38.990
in front of the x, a 1x,[br]which is really just saying

0:00:38.990,0:00:40.650
x over here?

0:00:40.650,0:00:42.860
Well, I'm dividing[br]it by 3 right now.

0:00:42.860,0:00:46.420
So if I were to multiply both[br]sides of this equation by 3,

0:00:46.420,0:00:47.680
that would isolate the x.

0:00:47.680,0:00:50.100
And the reason that would[br]work is if I multiply this

0:00:50.100,0:00:54.140
by 3 over here, I'm multiplying[br]by 3 and dividing by 3.

0:00:54.140,0:00:55.310
That's equivalent.

0:00:55.310,0:00:57.720
That's equivalent to[br]multiplying or dividing by 1.

0:00:57.720,0:00:58.995
These guys cancel out.

0:00:58.995,0:01:00.870
Remember, if you do it[br]to the left-hand side,

0:01:00.870,0:01:03.004
you also have to do it[br]to the right-hand side.

0:01:03.004,0:01:04.879
And actually, I'll do[br]both of these equations

0:01:04.879,0:01:06.545
at the same time,[br]because they're really

0:01:06.545,0:01:08.470
the exact same equation.

0:01:08.470,0:01:10.970
So what are we going to get[br]over here on the left-hand side?

0:01:10.970,0:01:15.350
3 times anything divided by 3[br]is going to be that anything.

0:01:15.350,0:01:17.580
We're just going to[br]have an x left over

0:01:17.580,0:01:19.050
on the left-hand side.

0:01:19.050,0:01:22.100
And on the right-hand[br]side, what's 14 times 3?

0:01:22.100,0:01:27.770
3 times 10 is 30,[br]3 times 4 is 12.

0:01:27.770,0:01:29.510
So it's going to be 42.

0:01:29.510,0:01:31.550
So we get x is equal to 42.

0:01:31.550,0:01:33.120
And the same thing[br]would happen here.

0:01:33.120,0:01:36.250
3 times 1/3 is just 1.

0:01:36.250,0:01:39.820
So you get 1x is equal to[br]14 times 3, which is 42.

0:01:39.820,0:01:41.250
Now let's just check our answer.

0:01:41.250,0:01:44.060
Let's substitute 42 into[br]our original equation.

0:01:44.060,0:01:52.190
So we have 42 in place for[br]x over 3 is equal to 14.

0:01:52.190,0:01:54.370
So what's 42 divided by 3?

0:01:54.370,0:01:57.210
And we could do a little[br]bit of-- I guess we call it

0:01:57.210,0:01:58.200
medium-long division.

0:01:58.200,0:01:59.690
It's not really long division.

0:01:59.690,0:02:01.210
3 into 4.

0:02:01.210,0:02:02.580
3 goes into 4 one time.

0:02:02.580,0:02:04.370
1 times 3 is 3.

0:02:04.370,0:02:05.250
You subtract.

0:02:05.250,0:02:07.100
4 minus 3 is 1.

0:02:07.100,0:02:08.370
Bring down the 2.

0:02:08.370,0:02:13.110
3 goes into 12 four times.

0:02:13.110,0:02:14.710
3 goes into 42 14 times.

0:02:14.710,0:02:19.230
So this right over[br]here simplifies to 14.

0:02:19.230,0:02:22.640
And it all checks[br]out, so we're done.