[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.61,0:00:03.18,Default,,0000,0000,0000,,Solve for a and\Ncheck your solution.
Dialogue: 0,0:00:03.18,0:00:06.05,Default,,0000,0000,0000,,And we have a plus\N5 is equal to 54.
Dialogue: 0,0:00:06.05,0:00:07.47,Default,,0000,0000,0000,,Now, all this is\Nsaying is that we
Dialogue: 0,0:00:07.47,0:00:10.31,Default,,0000,0000,0000,,have some numbers,\Nsome variable a.
Dialogue: 0,0:00:10.31,0:00:13.48,Default,,0000,0000,0000,,And if I add 5 to\Nit, I will get 54.
Dialogue: 0,0:00:13.48,0:00:15.40,Default,,0000,0000,0000,,And you might be able\Nto do this in your head.
Dialogue: 0,0:00:15.40,0:00:17.82,Default,,0000,0000,0000,,But we're going to do it a\Nlittle bit more systematically.
Dialogue: 0,0:00:17.82,0:00:19.57,Default,,0000,0000,0000,,Because that'll be\Nhelpful for you when we
Dialogue: 0,0:00:19.57,0:00:21.07,Default,,0000,0000,0000,,do more complicated problems.
Dialogue: 0,0:00:21.07,0:00:23.36,Default,,0000,0000,0000,,So in general, whenever you\Nhave an equation like this,
Dialogue: 0,0:00:23.36,0:00:24.93,Default,,0000,0000,0000,,we want to have the variable.
Dialogue: 0,0:00:24.93,0:00:29.67,Default,,0000,0000,0000,,We want this a all by itself\Non one side of the equation.
Dialogue: 0,0:00:29.67,0:00:31.36,Default,,0000,0000,0000,,We want to isolate it.
Dialogue: 0,0:00:31.36,0:00:32.82,Default,,0000,0000,0000,,It's already on\Nthe left-hand side,
Dialogue: 0,0:00:32.82,0:00:34.36,Default,,0000,0000,0000,,so let's try to get\Nrid of everything
Dialogue: 0,0:00:34.36,0:00:35.49,Default,,0000,0000,0000,,else on the left-hand side.
Dialogue: 0,0:00:35.49,0:00:37.49,Default,,0000,0000,0000,,Well, the only other thing\Non the left-hand side
Dialogue: 0,0:00:37.49,0:00:38.58,Default,,0000,0000,0000,,is this positive 5.
Dialogue: 0,0:00:38.58,0:00:42.44,Default,,0000,0000,0000,,Well, the best way to get rid\Nof a plus 5, or a positive 5,
Dialogue: 0,0:00:42.44,0:00:44.91,Default,,0000,0000,0000,,is to subtract 5.
Dialogue: 0,0:00:44.91,0:00:46.30,Default,,0000,0000,0000,,So let's subtract 5.
Dialogue: 0,0:00:46.30,0:00:50.11,Default,,0000,0000,0000,,But remember, this says\Na plus 5 is equal to 54.
Dialogue: 0,0:00:50.11,0:00:52.18,Default,,0000,0000,0000,,If we want the\Nequality to still hold,
Dialogue: 0,0:00:52.18,0:00:54.43,Default,,0000,0000,0000,,anything we do to the left-hand\Nside of this equation,
Dialogue: 0,0:00:54.43,0:00:57.55,Default,,0000,0000,0000,,we have to do to the right\Nside of the equation.
Dialogue: 0,0:00:57.55,0:01:00.66,Default,,0000,0000,0000,,So we also have to\Nsubtract 54 from the right.
Dialogue: 0,0:01:00.66,0:01:03.09,Default,,0000,0000,0000,,So we have a plus 5 minus 5.
Dialogue: 0,0:01:03.09,0:01:05.03,Default,,0000,0000,0000,,Well, that's just\Ngoing to be a plus 0.
Dialogue: 0,0:01:05.03,0:01:08.08,Default,,0000,0000,0000,,Because if you add 5 and you\Nsubtract 5, they cancel out.
Dialogue: 0,0:01:08.08,0:01:10.40,Default,,0000,0000,0000,,So a plus 0 is just a.
Dialogue: 0,0:01:10.40,0:01:14.52,Default,,0000,0000,0000,,And then 54 minus 5, that is 49.
Dialogue: 0,0:01:14.52,0:01:15.22,Default,,0000,0000,0000,,And we're done.
Dialogue: 0,0:01:15.22,0:01:16.98,Default,,0000,0000,0000,,We have solved for a.
Dialogue: 0,0:01:16.98,0:01:19.46,Default,,0000,0000,0000,,A is equal to 49.
Dialogue: 0,0:01:19.46,0:01:20.81,Default,,0000,0000,0000,,And now we can check it.
Dialogue: 0,0:01:20.81,0:01:24.27,Default,,0000,0000,0000,,And we can check it by\Njust substituting 49 back
Dialogue: 0,0:01:24.27,0:01:27.10,Default,,0000,0000,0000,,for a in our original equation.
Dialogue: 0,0:01:27.10,0:01:29.60,Default,,0000,0000,0000,,So instead of writing a\Nplus 5 is equal to 54,
Dialogue: 0,0:01:29.60,0:01:32.04,Default,,0000,0000,0000,,let's see if 49 plus\N5 is equal to 54.
Dialogue: 0,0:01:32.04,0:01:34.01,Default,,0000,0000,0000,,So we're just\Nsubstituting it back in.
Dialogue: 0,0:01:34.01,0:01:39.92,Default,,0000,0000,0000,,49, 49 plus-- let me do that\Nin that same shade of green.
Dialogue: 0,0:01:39.92,0:01:43.73,Default,,0000,0000,0000,,49 plus 5 is equal to 54.
Dialogue: 0,0:01:43.73,0:01:45.27,Default,,0000,0000,0000,,We're trying to check this.
Dialogue: 0,0:01:45.27,0:01:48.21,Default,,0000,0000,0000,,49 plus 5 is 54.
Dialogue: 0,0:01:48.21,0:01:51.14,Default,,0000,0000,0000,,And that, indeed,\Nis equal to 54.
Dialogue: 0,0:01:51.14,0:01:54.08,Default,,0000,0000,0000,,So it all checks out.