0:00:00.610,0:00:03.180
Solve for a and[br]check your solution.

0:00:03.180,0:00:06.054
And we have a plus[br]5 is equal to 54.

0:00:06.054,0:00:07.470
Now, all this is[br]saying is that we

0:00:07.470,0:00:10.310
have some numbers,[br]some variable a.

0:00:10.310,0:00:13.484
And if I add 5 to[br]it, I will get 54.

0:00:13.484,0:00:15.400
And you might be able[br]to do this in your head.

0:00:15.400,0:00:17.820
But we're going to do it a[br]little bit more systematically.

0:00:17.820,0:00:19.570
Because that'll be[br]helpful for you when we

0:00:19.570,0:00:21.070
do more complicated problems.

0:00:21.070,0:00:23.361
So in general, whenever you[br]have an equation like this,

0:00:23.361,0:00:24.930
we want to have the variable.

0:00:24.930,0:00:29.670
We want this a all by itself[br]on one side of the equation.

0:00:29.670,0:00:31.360
We want to isolate it.

0:00:31.360,0:00:32.819
It's already on[br]the left-hand side,

0:00:32.819,0:00:34.360
so let's try to get[br]rid of everything

0:00:34.360,0:00:35.490
else on the left-hand side.

0:00:35.490,0:00:37.490
Well, the only other thing[br]on the left-hand side

0:00:37.490,0:00:38.580
is this positive 5.

0:00:38.580,0:00:42.440
Well, the best way to get rid[br]of a plus 5, or a positive 5,

0:00:42.440,0:00:44.910
is to subtract 5.

0:00:44.910,0:00:46.300
So let's subtract 5.

0:00:46.300,0:00:50.110
But remember, this says[br]a plus 5 is equal to 54.

0:00:50.110,0:00:52.180
If we want the[br]equality to still hold,

0:00:52.180,0:00:54.430
anything we do to the left-hand[br]side of this equation,

0:00:54.430,0:00:57.550
we have to do to the right[br]side of the equation.

0:00:57.550,0:01:00.660
So we also have to[br]subtract 54 from the right.

0:01:00.660,0:01:03.090
So we have a plus 5 minus 5.

0:01:03.090,0:01:05.030
Well, that's just[br]going to be a plus 0.

0:01:05.030,0:01:08.080
Because if you add 5 and you[br]subtract 5, they cancel out.

0:01:08.080,0:01:10.400
So a plus 0 is just a.

0:01:10.400,0:01:14.520
And then 54 minus 5, that is 49.

0:01:14.520,0:01:15.220
And we're done.

0:01:15.220,0:01:16.975
We have solved for a.

0:01:16.975,0:01:19.460
A is equal to 49.

0:01:19.460,0:01:20.810
And now we can check it.

0:01:20.810,0:01:24.270
And we can check it by[br]just substituting 49 back

0:01:24.270,0:01:27.100
for a in our original equation.

0:01:27.100,0:01:29.600
So instead of writing a[br]plus 5 is equal to 54,

0:01:29.600,0:01:32.040
let's see if 49 plus[br]5 is equal to 54.

0:01:32.040,0:01:34.010
So we're just[br]substituting it back in.

0:01:34.010,0:01:39.920
49, 49 plus-- let me do that[br]in that same shade of green.

0:01:39.920,0:01:43.730
49 plus 5 is equal to 54.

0:01:43.730,0:01:45.270
We're trying to check this.

0:01:45.270,0:01:48.210
49 plus 5 is 54.

0:01:48.210,0:01:51.140
And that, indeed,[br]is equal to 54.

0:01:51.140,0:01:54.080
So it all checks out.