[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.76,0:00:03.37,Default,,0000,0000,0000,,Solve for x and\Ncheck your solution.
Dialogue: 0,0:00:03.37,0:00:07.92,Default,,0000,0000,0000,,We have x divided\Nby 3 is equal to 14.
Dialogue: 0,0:00:07.92,0:00:11.32,Default,,0000,0000,0000,,So to solve for x, to figure\Nout what the variable x must
Dialogue: 0,0:00:11.32,0:00:14.14,Default,,0000,0000,0000,,be equal to, we really\Njust have to isolate it
Dialogue: 0,0:00:14.14,0:00:15.76,Default,,0000,0000,0000,,on the left-hand side\Nof this equation.
Dialogue: 0,0:00:15.76,0:00:16.88,Default,,0000,0000,0000,,It's already sitting there.
Dialogue: 0,0:00:16.88,0:00:19.49,Default,,0000,0000,0000,,We have x divided\Nby 3 is equal to 14.
Dialogue: 0,0:00:19.49,0:00:24.96,Default,,0000,0000,0000,,We could also write this\Nas 1/3 x is equal to 14.
Dialogue: 0,0:00:24.96,0:00:27.73,Default,,0000,0000,0000,,Obviously, x times 1/3\Nis going to be x/3.
Dialogue: 0,0:00:27.73,0:00:28.84,Default,,0000,0000,0000,,These are equivalent.
Dialogue: 0,0:00:28.84,0:00:31.80,Default,,0000,0000,0000,,So how can we just end up with\Nan x on the left-hand side
Dialogue: 0,0:00:31.80,0:00:33.11,Default,,0000,0000,0000,,of either of these equations?
Dialogue: 0,0:00:33.11,0:00:34.44,Default,,0000,0000,0000,,These are really the same thing.
Dialogue: 0,0:00:34.44,0:00:36.37,Default,,0000,0000,0000,,Or another way, how\Ncan we just have a 1
Dialogue: 0,0:00:36.37,0:00:38.99,Default,,0000,0000,0000,,in front of the x, a 1x,\Nwhich is really just saying
Dialogue: 0,0:00:38.99,0:00:40.65,Default,,0000,0000,0000,,x over here?
Dialogue: 0,0:00:40.65,0:00:42.86,Default,,0000,0000,0000,,Well, I'm dividing\Nit by 3 right now.
Dialogue: 0,0:00:42.86,0:00:46.42,Default,,0000,0000,0000,,So if I were to multiply both\Nsides of this equation by 3,
Dialogue: 0,0:00:46.42,0:00:47.68,Default,,0000,0000,0000,,that would isolate the x.
Dialogue: 0,0:00:47.68,0:00:50.10,Default,,0000,0000,0000,,And the reason that would\Nwork is if I multiply this
Dialogue: 0,0:00:50.10,0:00:54.14,Default,,0000,0000,0000,,by 3 over here, I'm multiplying\Nby 3 and dividing by 3.
Dialogue: 0,0:00:54.14,0:00:55.31,Default,,0000,0000,0000,,That's equivalent.
Dialogue: 0,0:00:55.31,0:00:57.72,Default,,0000,0000,0000,,That's equivalent to\Nmultiplying or dividing by 1.
Dialogue: 0,0:00:57.72,0:00:58.100,Default,,0000,0000,0000,,These guys cancel out.
Dialogue: 0,0:00:58.100,0:01:00.87,Default,,0000,0000,0000,,Remember, if you do it\Nto the left-hand side,
Dialogue: 0,0:01:00.87,0:01:03.00,Default,,0000,0000,0000,,you also have to do it\Nto the right-hand side.
Dialogue: 0,0:01:03.00,0:01:04.88,Default,,0000,0000,0000,,And actually, I'll do\Nboth of these equations
Dialogue: 0,0:01:04.88,0:01:06.54,Default,,0000,0000,0000,,at the same time,\Nbecause they're really
Dialogue: 0,0:01:06.54,0:01:08.47,Default,,0000,0000,0000,,the exact same equation.
Dialogue: 0,0:01:08.47,0:01:10.97,Default,,0000,0000,0000,,So what are we going to get\Nover here on the left-hand side?
Dialogue: 0,0:01:10.97,0:01:15.35,Default,,0000,0000,0000,,3 times anything divided by 3\Nis going to be that anything.
Dialogue: 0,0:01:15.35,0:01:17.58,Default,,0000,0000,0000,,We're just going to\Nhave an x left over
Dialogue: 0,0:01:17.58,0:01:19.05,Default,,0000,0000,0000,,on the left-hand side.
Dialogue: 0,0:01:19.05,0:01:22.10,Default,,0000,0000,0000,,And on the right-hand\Nside, what's 14 times 3?
Dialogue: 0,0:01:22.10,0:01:27.77,Default,,0000,0000,0000,,3 times 10 is 30,\N3 times 4 is 12.
Dialogue: 0,0:01:27.77,0:01:29.51,Default,,0000,0000,0000,,So it's going to be 42.
Dialogue: 0,0:01:29.51,0:01:31.55,Default,,0000,0000,0000,,So we get x is equal to 42.
Dialogue: 0,0:01:31.55,0:01:33.12,Default,,0000,0000,0000,,And the same thing\Nwould happen here.
Dialogue: 0,0:01:33.12,0:01:36.25,Default,,0000,0000,0000,,3 times 1/3 is just 1.
Dialogue: 0,0:01:36.25,0:01:39.82,Default,,0000,0000,0000,,So you get 1x is equal to\N14 times 3, which is 42.
Dialogue: 0,0:01:39.82,0:01:41.25,Default,,0000,0000,0000,,Now let's just check our answer.
Dialogue: 0,0:01:41.25,0:01:44.06,Default,,0000,0000,0000,,Let's substitute 42 into\Nour original equation.
Dialogue: 0,0:01:44.06,0:01:52.19,Default,,0000,0000,0000,,So we have 42 in place for\Nx over 3 is equal to 14.
Dialogue: 0,0:01:52.19,0:01:54.37,Default,,0000,0000,0000,,So what's 42 divided by 3?
Dialogue: 0,0:01:54.37,0:01:57.21,Default,,0000,0000,0000,,And we could do a little\Nbit of-- I guess we call it
Dialogue: 0,0:01:57.21,0:01:58.20,Default,,0000,0000,0000,,medium-long division.
Dialogue: 0,0:01:58.20,0:01:59.69,Default,,0000,0000,0000,,It's not really long division.
Dialogue: 0,0:01:59.69,0:02:01.21,Default,,0000,0000,0000,,3 into 4.
Dialogue: 0,0:02:01.21,0:02:02.58,Default,,0000,0000,0000,,3 goes into 4 one time.
Dialogue: 0,0:02:02.58,0:02:04.37,Default,,0000,0000,0000,,1 times 3 is 3.
Dialogue: 0,0:02:04.37,0:02:05.25,Default,,0000,0000,0000,,You subtract.
Dialogue: 0,0:02:05.25,0:02:07.10,Default,,0000,0000,0000,,4 minus 3 is 1.
Dialogue: 0,0:02:07.10,0:02:08.37,Default,,0000,0000,0000,,Bring down the 2.
Dialogue: 0,0:02:08.37,0:02:13.11,Default,,0000,0000,0000,,3 goes into 12 four times.
Dialogue: 0,0:02:13.11,0:02:14.71,Default,,0000,0000,0000,,3 goes into 42 14 times.
Dialogue: 0,0:02:14.71,0:02:19.23,Default,,0000,0000,0000,,So this right over\Nhere simplifies to 14.
Dialogue: 0,0:02:19.23,0:02:22.64,Default,,0000,0000,0000,,And it all checks\Nout, so we're done.