[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.65,0:00:12.39,Default,,0000,0000,0000,,Let's say we have the equation\N7 times x is equal to 14.
Dialogue: 0,0:00:12.39,0:00:15.97,Default,,0000,0000,0000,,Now before even trying to solve\Nthis equation, what I want to
Dialogue: 0,0:00:15.97,0:00:20.08,Default,,0000,0000,0000,,do is think a little bit about\Nwhat this actually means.
Dialogue: 0,0:00:20.08,0:00:26.87,Default,,0000,0000,0000,,7x equals 14, this is the exact\Nsame thing as saying 7 times x
Dialogue: 0,0:00:26.87,0:00:35.00,Default,,0000,0000,0000,,-- let me write it this way --\N7 times x -- we'll do the x in
Dialogue: 0,0:00:35.00,0:00:41.27,Default,,0000,0000,0000,,orange again -- 7 times\Nx is equal to 14.
Dialogue: 0,0:00:41.27,0:00:42.86,Default,,0000,0000,0000,,Now you might be able to\Ndo this in your head.
Dialogue: 0,0:00:42.86,0:00:45.49,Default,,0000,0000,0000,,You could literally go\Nthrough the 7 times table.
Dialogue: 0,0:00:45.49,0:00:48.96,Default,,0000,0000,0000,,You say well 7 times 1 is equal\Nto 7, so that won't work.
Dialogue: 0,0:00:48.96,0:00:54.35,Default,,0000,0000,0000,,7 times 2 is equal to\N14, so 2 works here.
Dialogue: 0,0:00:54.35,0:00:55.92,Default,,0000,0000,0000,,So you would immediately\Nbe able to solve it.
Dialogue: 0,0:00:55.92,0:00:58.51,Default,,0000,0000,0000,,You would immediately, just\Nby trying different numbers
Dialogue: 0,0:00:58.51,0:01:01.22,Default,,0000,0000,0000,,out, say hey, that's\Ngoing to be a 2.
Dialogue: 0,0:01:01.22,0:01:03.20,Default,,0000,0000,0000,,But what we're going to do in\Nthis video is to think about
Dialogue: 0,0:01:03.20,0:01:04.78,Default,,0000,0000,0000,,how to solve this\Nsystematically.
Dialogue: 0,0:01:04.78,0:01:07.10,Default,,0000,0000,0000,,Because what we're going to\Nfind is as these equations get
Dialogue: 0,0:01:07.10,0:01:09.68,Default,,0000,0000,0000,,more and more complicated,\Nyou're not going to be able to
Dialogue: 0,0:01:09.68,0:01:11.67,Default,,0000,0000,0000,,just think about it and\Ndo it in your head.
Dialogue: 0,0:01:11.67,0:01:14.59,Default,,0000,0000,0000,,So it's really important that\None, you understand how to
Dialogue: 0,0:01:14.59,0:01:16.51,Default,,0000,0000,0000,,manipulate these equations,\Nbut even more important to
Dialogue: 0,0:01:16.51,0:01:18.28,Default,,0000,0000,0000,,understand what they\Nactually represent.
Dialogue: 0,0:01:18.28,0:01:22.09,Default,,0000,0000,0000,,This literally just says 7\Ntimes x is equal to 14.
Dialogue: 0,0:01:22.09,0:01:24.53,Default,,0000,0000,0000,,In algebra we don't\Nwrite the times there.
Dialogue: 0,0:01:24.53,0:01:27.62,Default,,0000,0000,0000,,When you write two numbers next\Nto each other or a number next
Dialogue: 0,0:01:27.62,0:01:30.28,Default,,0000,0000,0000,,to a variable like this, it\Njust means that you
Dialogue: 0,0:01:30.28,0:01:31.10,Default,,0000,0000,0000,,are multiplying.
Dialogue: 0,0:01:31.10,0:01:33.92,Default,,0000,0000,0000,,It's just a shorthand,\Na shorthand notation.
Dialogue: 0,0:01:33.92,0:01:37.04,Default,,0000,0000,0000,,And in general we don't use the\Nmultiplication sign because
Dialogue: 0,0:01:37.04,0:01:40.97,Default,,0000,0000,0000,,it's confusing, because x is\Nthe most common variable
Dialogue: 0,0:01:40.97,0:01:41.84,Default,,0000,0000,0000,,used in algebra.
Dialogue: 0,0:01:41.84,0:01:49.33,Default,,0000,0000,0000,,And if I were to write 7 times\Nx is equal to 14, if I write my
Dialogue: 0,0:01:49.33,0:01:52.14,Default,,0000,0000,0000,,times sign or my x a little\Nbit strange, it might look
Dialogue: 0,0:01:52.14,0:01:54.15,Default,,0000,0000,0000,,like xx or times times.
Dialogue: 0,0:01:54.15,0:01:56.41,Default,,0000,0000,0000,,So in general when you're\Ndealing with equations,
Dialogue: 0,0:01:56.41,0:01:58.91,Default,,0000,0000,0000,,especially when one of the\Nvariables is an x, you
Dialogue: 0,0:01:58.91,0:02:01.35,Default,,0000,0000,0000,,wouldn't use the traditional\Nmultiplication sign.
Dialogue: 0,0:02:01.35,0:02:05.02,Default,,0000,0000,0000,,You might use something like\Nthis -- you might use dot to
Dialogue: 0,0:02:05.02,0:02:06.13,Default,,0000,0000,0000,,represent multiplication.
Dialogue: 0,0:02:06.13,0:02:10.04,Default,,0000,0000,0000,,So you might have 7\Ntimes is equal to 14.
Dialogue: 0,0:02:10.04,0:02:11.72,Default,,0000,0000,0000,,But this is still\Na little unusual.
Dialogue: 0,0:02:11.72,0:02:13.75,Default,,0000,0000,0000,,If you have something\Nmultiplying by a variable
Dialogue: 0,0:02:13.75,0:02:15.08,Default,,0000,0000,0000,,you'll just write 7x.
Dialogue: 0,0:02:15.08,0:02:18.21,Default,,0000,0000,0000,,That literally means 7 times x.
Dialogue: 0,0:02:18.21,0:02:22.75,Default,,0000,0000,0000,,Now, to understand how you can\Nmanipulate this equation to
Dialogue: 0,0:02:22.75,0:02:25.04,Default,,0000,0000,0000,,solve it, let's visualize this.
Dialogue: 0,0:02:25.04,0:02:27.71,Default,,0000,0000,0000,,So 7 times x, what is that?
Dialogue: 0,0:02:27.71,0:02:29.69,Default,,0000,0000,0000,,That's the same thing -- so I'm\Njust going to re-write this
Dialogue: 0,0:02:29.69,0:02:32.72,Default,,0000,0000,0000,,equation, but I'm going to\Nre-write it in visual form.
Dialogue: 0,0:02:32.72,0:02:34.88,Default,,0000,0000,0000,,So 7 times x.
Dialogue: 0,0:02:34.88,0:02:37.74,Default,,0000,0000,0000,,So that literally means x\Nadded to itself 7 times.
Dialogue: 0,0:02:37.74,0:02:40.23,Default,,0000,0000,0000,,That's the definition\Nof multiplication.
Dialogue: 0,0:02:40.23,0:02:47.90,Default,,0000,0000,0000,,So it's literally x plus x plus\Nx plus x plus x -- let's see,
Dialogue: 0,0:02:47.90,0:02:51.83,Default,,0000,0000,0000,,that's 5 x's -- plus x plus x.
Dialogue: 0,0:02:51.83,0:02:54.66,Default,,0000,0000,0000,,So that right there\Nis literally 7 x's.
Dialogue: 0,0:02:54.66,0:02:56.30,Default,,0000,0000,0000,,This is 7x right there.
Dialogue: 0,0:02:56.30,0:02:57.27,Default,,0000,0000,0000,,Let me re-write it down.
Dialogue: 0,0:02:57.27,0:03:03.03,Default,,0000,0000,0000,,This right here is 7x.
Dialogue: 0,0:03:03.03,0:03:07.61,Default,,0000,0000,0000,,Now this equation tells us\Nthat 7x is equal to 14.
Dialogue: 0,0:03:07.61,0:03:10.80,Default,,0000,0000,0000,,So just saying that\Nthis is equal to 14.
Dialogue: 0,0:03:10.80,0:03:13.30,Default,,0000,0000,0000,,Let me draw 14 objects here.
Dialogue: 0,0:03:13.30,0:03:19.64,Default,,0000,0000,0000,,So let's say I have 1,\N2, 3, 4, 5, 6, 7, 8,
Dialogue: 0,0:03:19.64,0:03:23.64,Default,,0000,0000,0000,,9, 10, 11, 12, 13, 14.
Dialogue: 0,0:03:23.64,0:03:26.79,Default,,0000,0000,0000,,So literally we're saying\N7x is equal to 14 things.
Dialogue: 0,0:03:26.79,0:03:29.07,Default,,0000,0000,0000,,These are equivalent\Nstatements.
Dialogue: 0,0:03:29.07,0:03:32.28,Default,,0000,0000,0000,,Now the reason why I drew\Nit out this way is so that
Dialogue: 0,0:03:32.28,0:03:34.95,Default,,0000,0000,0000,,you really understand what\Nwe're going to do when we
Dialogue: 0,0:03:34.95,0:03:37.11,Default,,0000,0000,0000,,divide both sides by 7.
Dialogue: 0,0:03:37.11,0:03:39.82,Default,,0000,0000,0000,,So let me erase\Nthis right here.
Dialogue: 0,0:03:39.82,0:03:44.18,Default,,0000,0000,0000,,So the standard step whenever\N-- I didn't want to do that,
Dialogue: 0,0:03:44.18,0:03:48.72,Default,,0000,0000,0000,,let me do this, let me\Ndraw that last circle.
Dialogue: 0,0:03:48.72,0:03:52.36,Default,,0000,0000,0000,,So in general, whenever you\Nsimplify an equation down to a
Dialogue: 0,0:03:52.36,0:03:55.08,Default,,0000,0000,0000,,-- a coefficient is just the\Nnumber multiplying
Dialogue: 0,0:03:55.08,0:03:55.75,Default,,0000,0000,0000,,the variable.
Dialogue: 0,0:03:55.75,0:03:58.46,Default,,0000,0000,0000,,So some number multiplying the\Nvariable or we could call that
Dialogue: 0,0:03:58.46,0:04:00.99,Default,,0000,0000,0000,,the coefficient times a\Nvariable equal to
Dialogue: 0,0:04:00.99,0:04:01.99,Default,,0000,0000,0000,,something else.
Dialogue: 0,0:04:01.99,0:04:05.21,Default,,0000,0000,0000,,What you want to do is just\Ndivide both sides by 7 in
Dialogue: 0,0:04:05.21,0:04:08.24,Default,,0000,0000,0000,,this case, or divide both\Nsides by the coefficient.
Dialogue: 0,0:04:08.24,0:04:12.13,Default,,0000,0000,0000,,So if you divide both sides\Nby 7, what do you get?
Dialogue: 0,0:04:12.13,0:04:16.15,Default,,0000,0000,0000,,7 times something divided\Nby 7 is just going to be
Dialogue: 0,0:04:16.15,0:04:17.69,Default,,0000,0000,0000,,that original something.
Dialogue: 0,0:04:17.69,0:04:22.35,Default,,0000,0000,0000,,7's cancel out and 14\Ndivided by 7 is 2.
Dialogue: 0,0:04:22.35,0:04:26.18,Default,,0000,0000,0000,,So your solution is going\Nto be x is equal to 2.
Dialogue: 0,0:04:26.18,0:04:29.20,Default,,0000,0000,0000,,But just to make it very\Ntangible in your head, what's
Dialogue: 0,0:04:29.20,0:04:32.57,Default,,0000,0000,0000,,going on here is when we're\Ndividing both sides of the
Dialogue: 0,0:04:32.57,0:04:36.26,Default,,0000,0000,0000,,equation by 7, we're literally\Ndividing both sides by 7.
Dialogue: 0,0:04:36.26,0:04:37.25,Default,,0000,0000,0000,,This is an equation.
Dialogue: 0,0:04:37.25,0:04:39.85,Default,,0000,0000,0000,,It's saying that this\Nis equal to that.
Dialogue: 0,0:04:39.85,0:04:43.23,Default,,0000,0000,0000,,Anything I do to the left hand\Nside I have to do to the right.
Dialogue: 0,0:04:43.23,0:04:46.13,Default,,0000,0000,0000,,If they start off being equal,\NI can't just do an operation
Dialogue: 0,0:04:46.13,0:04:48.97,Default,,0000,0000,0000,,to one side and have\Nit still be equal.
Dialogue: 0,0:04:48.97,0:04:50.10,Default,,0000,0000,0000,,They were the same thing.
Dialogue: 0,0:04:50.10,0:04:53.42,Default,,0000,0000,0000,,So if I divide the left hand\Nside by 7, so let me divide
Dialogue: 0,0:04:53.42,0:04:55.15,Default,,0000,0000,0000,,it into seven groups.
Dialogue: 0,0:04:55.15,0:04:58.92,Default,,0000,0000,0000,,So there are seven x's here,\Nso that's one, two, three,
Dialogue: 0,0:04:58.92,0:05:01.69,Default,,0000,0000,0000,,four, five, six, seven.
Dialogue: 0,0:05:01.69,0:05:04.78,Default,,0000,0000,0000,,So it's one, two, three, four,\Nfive, six, seven groups.
Dialogue: 0,0:05:04.78,0:05:07.24,Default,,0000,0000,0000,,Now if I divide that into\Nseven groups, I'll also want
Dialogue: 0,0:05:07.24,0:05:11.35,Default,,0000,0000,0000,,to divide the right hand\Nside into seven groups.
Dialogue: 0,0:05:11.35,0:05:16.53,Default,,0000,0000,0000,,One, two, three, four,\Nfive, six, seven.
Dialogue: 0,0:05:16.53,0:05:20.37,Default,,0000,0000,0000,,So if this whole thing is equal\Nto this whole thing, then each
Dialogue: 0,0:05:20.37,0:05:25.66,Default,,0000,0000,0000,,of these little chunks that we\Nbroke into, these seven chunks,
Dialogue: 0,0:05:25.66,0:05:27.86,Default,,0000,0000,0000,,are going to be equivalent.
Dialogue: 0,0:05:27.86,0:05:32.07,Default,,0000,0000,0000,,So this chunk you could say\Nis equal to that chunk.
Dialogue: 0,0:05:32.07,0:05:34.53,Default,,0000,0000,0000,,This chunk is equal to\Nthis chunk -- they're
Dialogue: 0,0:05:34.53,0:05:35.49,Default,,0000,0000,0000,,all equivalent chunks.
Dialogue: 0,0:05:35.49,0:05:37.36,Default,,0000,0000,0000,,There are seven chunks\Nhere, seven chunks here.
Dialogue: 0,0:05:37.36,0:05:41.39,Default,,0000,0000,0000,,So each x must be equal\Nto two of these objects.
Dialogue: 0,0:05:41.39,0:05:46.24,Default,,0000,0000,0000,,So we get x is equal to, in\Nthis case -- in this case
Dialogue: 0,0:05:46.24,0:05:48.83,Default,,0000,0000,0000,,we had the objects drawn\Nout where there's two of
Dialogue: 0,0:05:48.83,0:05:50.68,Default,,0000,0000,0000,,them. x is equal to 2.
Dialogue: 0,0:05:50.68,0:05:53.21,Default,,0000,0000,0000,,Now, let's just do a couple\Nmore examples here just so it
Dialogue: 0,0:05:53.21,0:05:55.56,Default,,0000,0000,0000,,really gets in your mind that\Nwe're dealing with an equation,
Dialogue: 0,0:05:55.56,0:05:58.32,Default,,0000,0000,0000,,and any operation that you do\Non one side of the equation
Dialogue: 0,0:05:58.32,0:06:00.54,Default,,0000,0000,0000,,you should do to the other.
Dialogue: 0,0:06:00.54,0:06:04.04,Default,,0000,0000,0000,,So let me scroll\Ndown a little bit.
Dialogue: 0,0:06:04.04,0:06:13.55,Default,,0000,0000,0000,,So let's say I have I say\NI have 3x is equal to 15.
Dialogue: 0,0:06:13.55,0:06:15.64,Default,,0000,0000,0000,,Now once again, you might be\Nable to do is in your head.
Dialogue: 0,0:06:15.64,0:06:17.78,Default,,0000,0000,0000,,You're saying this is\Nsaying 3 times some
Dialogue: 0,0:06:17.78,0:06:19.49,Default,,0000,0000,0000,,number is equal to 15.
Dialogue: 0,0:06:19.49,0:06:22.38,Default,,0000,0000,0000,,You could go through your 3\Ntimes tables and figure it out.
Dialogue: 0,0:06:22.38,0:06:25.15,Default,,0000,0000,0000,,But if you just wanted to do\Nthis systematically, and it
Dialogue: 0,0:06:25.15,0:06:27.68,Default,,0000,0000,0000,,is good to understand it\Nsystematically, say OK, this
Dialogue: 0,0:06:27.68,0:06:30.50,Default,,0000,0000,0000,,thing on the left is equal\Nto this thing on the right.
Dialogue: 0,0:06:30.50,0:06:31.100,Default,,0000,0000,0000,,What do I have to do to\Nthis thing on the left
Dialogue: 0,0:06:31.100,0:06:33.64,Default,,0000,0000,0000,,to have just an x there?
Dialogue: 0,0:06:33.64,0:06:36.69,Default,,0000,0000,0000,,Well to have just an x there,\NI want to divide it by 3.
Dialogue: 0,0:06:36.69,0:06:39.93,Default,,0000,0000,0000,,And my whole motivation for\Ndoing that is that 3 times
Dialogue: 0,0:06:39.93,0:06:43.62,Default,,0000,0000,0000,,something divided by 3, the 3's\Nwill cancel out and I'm just
Dialogue: 0,0:06:43.62,0:06:45.12,Default,,0000,0000,0000,,going to be left with an x.
Dialogue: 0,0:06:45.12,0:06:48.19,Default,,0000,0000,0000,,Now, 3x was equal to 15.
Dialogue: 0,0:06:48.19,0:06:52.24,Default,,0000,0000,0000,,If I'm dividing the left side\Nby 3, in order for the equality
Dialogue: 0,0:06:52.24,0:06:57.23,Default,,0000,0000,0000,,to still hold, I also have to\Ndivide the right side by 3.
Dialogue: 0,0:06:57.23,0:06:58.56,Default,,0000,0000,0000,,Now what does that give us?
Dialogue: 0,0:06:58.56,0:07:01.07,Default,,0000,0000,0000,,Well the left hand side, we're\Njust going to be left with
Dialogue: 0,0:07:01.07,0:07:04.13,Default,,0000,0000,0000,,an x, so it's just\Ngoing to be an x.
Dialogue: 0,0:07:04.13,0:07:08.04,Default,,0000,0000,0000,,And then the right hand side,\Nwhat is 15 divided by 3?
Dialogue: 0,0:07:08.04,0:07:10.76,Default,,0000,0000,0000,,Well it is just 5.
Dialogue: 0,0:07:10.76,0:07:13.57,Default,,0000,0000,0000,,Now you could also done this\Nequation in a slightly
Dialogue: 0,0:07:13.57,0:07:16.14,Default,,0000,0000,0000,,different way, although they\Nare really equivalent.
Dialogue: 0,0:07:16.14,0:07:21.16,Default,,0000,0000,0000,,If I start with 3x is equal to\N15, you might say hey, Sal,
Dialogue: 0,0:07:21.16,0:07:25.26,Default,,0000,0000,0000,,instead of dividing by 3, I\Ncould also get rid of this 3, I
Dialogue: 0,0:07:25.26,0:07:28.11,Default,,0000,0000,0000,,could just be left with an x if\NI multiply both sides of
Dialogue: 0,0:07:28.11,0:07:30.67,Default,,0000,0000,0000,,this equation by 1/3.
Dialogue: 0,0:07:30.67,0:07:34.71,Default,,0000,0000,0000,,So if I multiply both sides\Nof this equation by 1/3
Dialogue: 0,0:07:34.71,0:07:35.83,Default,,0000,0000,0000,,that should also work.
Dialogue: 0,0:07:35.83,0:07:38.98,Default,,0000,0000,0000,,You say look, 1/3 of 3 is 1.
Dialogue: 0,0:07:38.98,0:07:41.71,Default,,0000,0000,0000,,When you just multiply this\Npart right here, 1/3 times
Dialogue: 0,0:07:41.71,0:07:46.17,Default,,0000,0000,0000,,3, that is just 1, 1x.
Dialogue: 0,0:07:46.17,0:07:52.13,Default,,0000,0000,0000,,1x is equal to 15 times\N1/3 third is equal to 5.
Dialogue: 0,0:07:52.13,0:07:56.14,Default,,0000,0000,0000,,And 1 times x is the same thing\Nas just x, so this is the same
Dialogue: 0,0:07:56.14,0:07:58.40,Default,,0000,0000,0000,,thing as x is equal to 5.
Dialogue: 0,0:07:58.40,0:08:01.66,Default,,0000,0000,0000,,And these are actually\Nequivalent ways of doing it.
Dialogue: 0,0:08:01.66,0:08:05.18,Default,,0000,0000,0000,,If you divide both sides by\N3, that is equivalent to
Dialogue: 0,0:08:05.18,0:08:10.34,Default,,0000,0000,0000,,multiplying both sides\Nof the equation by 1/3.
Dialogue: 0,0:08:10.34,0:08:12.16,Default,,0000,0000,0000,,Now let's do one more and I'm\Ngoing to make it a little
Dialogue: 0,0:08:12.16,0:08:15.27,Default,,0000,0000,0000,,bit more complicated.
Dialogue: 0,0:08:15.27,0:08:16.84,Default,,0000,0000,0000,,And I'm going to change the\Nvariable a little bit.
Dialogue: 0,0:08:16.84,0:08:36.20,Default,,0000,0000,0000,,So let's say I have 2y\Nplus 4y is equal to 18.
Dialogue: 0,0:08:36.20,0:08:37.96,Default,,0000,0000,0000,,Now all of a sudden it's\Na little harder to
Dialogue: 0,0:08:37.96,0:08:38.54,Default,,0000,0000,0000,,do it in your head.
Dialogue: 0,0:08:38.54,0:08:42.42,Default,,0000,0000,0000,,We're saying 2 times something\Nplus 4 times that same
Dialogue: 0,0:08:42.42,0:08:45.26,Default,,0000,0000,0000,,something is going\Nto be equal to 18.
Dialogue: 0,0:08:45.26,0:08:47.40,Default,,0000,0000,0000,,So it's harder to think\Nabout what number that is.
Dialogue: 0,0:08:47.40,0:08:48.11,Default,,0000,0000,0000,,You could try them.
Dialogue: 0,0:08:48.11,0:08:51.91,Default,,0000,0000,0000,,Say if y was 1, it'd be 2\Ntimes 1 plus 4 times 1,
Dialogue: 0,0:08:51.91,0:08:52.71,Default,,0000,0000,0000,,well that doesn't work.
Dialogue: 0,0:08:52.71,0:08:54.39,Default,,0000,0000,0000,,But let's think about how\Nto do it systematically.
Dialogue: 0,0:08:54.39,0:08:56.25,Default,,0000,0000,0000,,You could keep guessing and\Nyou might eventually get
Dialogue: 0,0:08:56.25,0:08:58.84,Default,,0000,0000,0000,,the answer, but how do you\Ndo this systematically.
Dialogue: 0,0:08:58.84,0:08:59.83,Default,,0000,0000,0000,,Let's visualize it.
Dialogue: 0,0:08:59.83,0:09:04.54,Default,,0000,0000,0000,,So if I have two y's,\Nwhat does that mean?
Dialogue: 0,0:09:04.54,0:09:08.80,Default,,0000,0000,0000,,It literally means I have two\Ny's added to each other.
Dialogue: 0,0:09:08.80,0:09:11.99,Default,,0000,0000,0000,,So it's literally y plus y.
Dialogue: 0,0:09:11.99,0:09:15.30,Default,,0000,0000,0000,,And then to that I'm\Nadding four y's.
Dialogue: 0,0:09:15.30,0:09:18.35,Default,,0000,0000,0000,,To that I'm heading four y's,\Nwhich are literally four
Dialogue: 0,0:09:18.35,0:09:20.09,Default,,0000,0000,0000,,y's added to each other.
Dialogue: 0,0:09:20.09,0:09:25.22,Default,,0000,0000,0000,,So it's y plus y plus y plus y.
Dialogue: 0,0:09:25.22,0:09:28.63,Default,,0000,0000,0000,,And that has got to\Nbe equal to 18.
Dialogue: 0,0:09:28.63,0:09:34.53,Default,,0000,0000,0000,,So that is equal to 18.
Dialogue: 0,0:09:34.53,0:09:38.84,Default,,0000,0000,0000,,Now, how many y's do I have\Nhere on the left hand side?
Dialogue: 0,0:09:38.84,0:09:41.52,Default,,0000,0000,0000,,How many y's do I have?
Dialogue: 0,0:09:41.52,0:09:45.59,Default,,0000,0000,0000,,I have one, two, three,\Nfour, five, six y's.
Dialogue: 0,0:09:45.59,0:09:49.07,Default,,0000,0000,0000,,So you could simplify this\Nas 6y is equal to 18.
Dialogue: 0,0:09:49.07,0:09:50.93,Default,,0000,0000,0000,,And if you think about it\Nit makes complete sense.
Dialogue: 0,0:09:50.93,0:09:57.35,Default,,0000,0000,0000,,So this thing right here,\Nthe 2y plus the 4y is 6y.
Dialogue: 0,0:09:57.35,0:10:00.32,Default,,0000,0000,0000,,So 2y plus 4y is 6y,\Nwhich makes sense.
Dialogue: 0,0:10:00.32,0:10:02.84,Default,,0000,0000,0000,,If I have 2 apples plus\N4 apples, I'm going
Dialogue: 0,0:10:02.84,0:10:03.85,Default,,0000,0000,0000,,to have 6 apples.
Dialogue: 0,0:10:03.85,0:10:07.81,Default,,0000,0000,0000,,If I have 2 y's plus 4 y's\NI'm going to have 6 y's.
Dialogue: 0,0:10:07.81,0:10:09.62,Default,,0000,0000,0000,,Now that's going to\Nbe equal to 18.
Dialogue: 0,0:10:12.27,0:10:15.25,Default,,0000,0000,0000,,And now, hopefully, we\Nunderstand how to do this.
Dialogue: 0,0:10:15.25,0:10:18.49,Default,,0000,0000,0000,,If I have 6 times something is\Nequal to 18, if I divide both
Dialogue: 0,0:10:18.49,0:10:22.71,Default,,0000,0000,0000,,sides of this equation by 6,\NI'll solve for the something.
Dialogue: 0,0:10:22.71,0:10:29.92,Default,,0000,0000,0000,,So divide the left hand\Nside by 6, and divide the
Dialogue: 0,0:10:29.92,0:10:31.87,Default,,0000,0000,0000,,right hand side by 6.
Dialogue: 0,0:10:31.87,0:10:39.10,Default,,0000,0000,0000,,And we are left with\Ny is equal to 3.
Dialogue: 0,0:10:39.10,0:10:40.16,Default,,0000,0000,0000,,And you could try it out.
Dialogue: 0,0:10:40.16,0:10:41.75,Default,,0000,0000,0000,,That's what's cool\Nabout an equation.
Dialogue: 0,0:10:41.75,0:10:44.29,Default,,0000,0000,0000,,You can always check to see\Nif you got the right answer.
Dialogue: 0,0:10:44.29,0:10:45.22,Default,,0000,0000,0000,,Let's see if that works.
Dialogue: 0,0:10:45.22,0:10:52.12,Default,,0000,0000,0000,,2 times 3 plus 4 times\N3 is equal to what?
Dialogue: 0,0:10:52.12,0:10:56.64,Default,,0000,0000,0000,,2 times 3, this\Nright here is 6.
Dialogue: 0,0:10:56.64,0:10:59.58,Default,,0000,0000,0000,,And then 4 times 3 is 12.
Dialogue: 0,0:10:59.58,0:11:03.41,Default,,0000,0000,0000,,6 plus 12 is, indeed,\Nequal to 18.
Dialogue: 0,0:11:03.41,0:11:05.64,Default,,0000,0000,0000,,So it works out.