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[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.23,0:00:04.28,Default,,0000,0000,0000,,Welcome to the presentation on\Nlevel four linear equations.
Dialogue: 0,0:00:04.28,0:00:06.54,Default,,0000,0000,0000,,So, let's start doing\Nsome problems.
Dialogue: 0,0:00:06.54,0:00:06.71,Default,,0000,0000,0000,,So.
Dialogue: 0,0:00:06.71,0:00:09.58,Default,,0000,0000,0000,,Let's say I had the situation--\Nlet me give me a couple of
Dialogue: 0,0:00:09.58,0:00:20.11,Default,,0000,0000,0000,,problems-- if I said 3 over x\Nis equal to, let's just say 5.
Dialogue: 0,0:00:20.11,0:00:23.18,Default,,0000,0000,0000,,So, what we want to do -- this\Nproblem's a little unusual from
Dialogue: 0,0:00:23.18,0:00:24.26,Default,,0000,0000,0000,,everything we've ever seen.
Dialogue: 0,0:00:24.26,0:00:26.95,Default,,0000,0000,0000,,Because here, instead of having\Nx in the numerator, we actually
Dialogue: 0,0:00:26.95,0:00:28.15,Default,,0000,0000,0000,,have x in the denominator.
Dialogue: 0,0:00:28.15,0:00:31.27,Default,,0000,0000,0000,,So, I personally don't like\Nhaving x's in my denominators,
Dialogue: 0,0:00:31.27,0:00:34.19,Default,,0000,0000,0000,,so we want to get it outside of\Nthe denominator into a
Dialogue: 0,0:00:34.19,0:00:36.14,Default,,0000,0000,0000,,numerator or at least not in\Nthe denominator as
Dialogue: 0,0:00:36.14,0:00:36.92,Default,,0000,0000,0000,,soon as possible.
Dialogue: 0,0:00:36.92,0:00:40.78,Default,,0000,0000,0000,,So, one way to get a number out\Nof the denominator is, if we
Dialogue: 0,0:00:40.78,0:00:45.56,Default,,0000,0000,0000,,were to multiply both sides of\Nthis equation by x, you see
Dialogue: 0,0:00:45.56,0:00:47.46,Default,,0000,0000,0000,,that on the left-hand side of\Nthe equation these two
Dialogue: 0,0:00:47.46,0:00:48.90,Default,,0000,0000,0000,,x's will cancel out.
Dialogue: 0,0:00:48.90,0:00:52.16,Default,,0000,0000,0000,,And in the right side,\Nyou'll just get 5 times x.
Dialogue: 0,0:00:52.16,0:00:56.92,Default,,0000,0000,0000,,So this equals -- the\Ntwo x's cancel out.
Dialogue: 0,0:00:56.92,0:01:00.89,Default,,0000,0000,0000,,And you get 3 is equal to 5x.
Dialogue: 0,0:01:00.89,0:01:05.42,Default,,0000,0000,0000,,Now, we could also write\Nthat as 5x is equal to 3.
Dialogue: 0,0:01:05.42,0:01:07.81,Default,,0000,0000,0000,,And then we can think\Nabout this two ways.
Dialogue: 0,0:01:07.81,0:01:12.21,Default,,0000,0000,0000,,We either just multiply both\Nsides by 1/5, or you could just
Dialogue: 0,0:01:12.21,0:01:14.23,Default,,0000,0000,0000,,do that as dividing by 5.
Dialogue: 0,0:01:14.23,0:01:16.49,Default,,0000,0000,0000,,If you multiply\Nboth sides by 1/5.
Dialogue: 0,0:01:16.49,0:01:18.68,Default,,0000,0000,0000,,The left-hand side becomes x.
Dialogue: 0,0:01:18.68,0:01:23.74,Default,,0000,0000,0000,,And the right-hand side, 3\Ntimes 1/5, is equal to 3/5.
Dialogue: 0,0:01:23.74,0:01:24.64,Default,,0000,0000,0000,,So what did we do here?
Dialogue: 0,0:01:24.64,0:01:26.86,Default,,0000,0000,0000,,This is just like, this\Nactually turned into a level
Dialogue: 0,0:01:26.86,0:01:28.67,Default,,0000,0000,0000,,two problem, or actually a\Nlevel one problem,
Dialogue: 0,0:01:28.67,0:01:29.48,Default,,0000,0000,0000,,very quickly.
Dialogue: 0,0:01:29.48,0:01:31.99,Default,,0000,0000,0000,,All we had to do is multiply\Nboth sides of this
Dialogue: 0,0:01:31.99,0:01:33.26,Default,,0000,0000,0000,,equation by x.
Dialogue: 0,0:01:33.26,0:01:35.46,Default,,0000,0000,0000,,And we got the x's out\Nof the denominator.
Dialogue: 0,0:01:35.46,0:01:36.36,Default,,0000,0000,0000,,Let's do another problem.
Dialogue: 0,0:01:41.11,0:01:53.53,Default,,0000,0000,0000,,Let's have -- let me say,\Nx plus 2 over x plus 1 is
Dialogue: 0,0:01:53.53,0:01:58.80,Default,,0000,0000,0000,,equal to, let's say, 7.
Dialogue: 0,0:01:58.80,0:02:00.79,Default,,0000,0000,0000,,So, here, instead of having\Njust an x in the denominator,
Dialogue: 0,0:02:00.79,0:02:02.92,Default,,0000,0000,0000,,we have a whole x plus\N1 in the denominator.
Dialogue: 0,0:02:02.92,0:02:05.00,Default,,0000,0000,0000,,But we're going to\Ndo it the same way.
Dialogue: 0,0:02:05.00,0:02:09.17,Default,,0000,0000,0000,,To get that x plus 1 out of the\Ndenominator, we multiply both
Dialogue: 0,0:02:09.17,0:02:15.45,Default,,0000,0000,0000,,sides of this equation times x\Nplus 1 over 1 times this side.
Dialogue: 0,0:02:15.45,0:02:17.01,Default,,0000,0000,0000,,Since we did it on the\Nleft-hand side we also have
Dialogue: 0,0:02:17.01,0:02:19.64,Default,,0000,0000,0000,,to do it on the right-hand\Nside, and this is just 7/1,
Dialogue: 0,0:02:19.64,0:02:24.42,Default,,0000,0000,0000,,times x plus 1 over 1.
Dialogue: 0,0:02:24.42,0:02:27.72,Default,,0000,0000,0000,,On the left-hand side, the\Nx plus 1's cancel out.
Dialogue: 0,0:02:27.72,0:02:31.11,Default,,0000,0000,0000,,And you're just left\Nwith x plus 2.
Dialogue: 0,0:02:31.11,0:02:33.30,Default,,0000,0000,0000,,It's over 1, but we can\Njust ignore the 1.
Dialogue: 0,0:02:33.30,0:02:39.26,Default,,0000,0000,0000,,And that equals 7\Ntimes x plus 1.
Dialogue: 0,0:02:39.26,0:02:41.93,Default,,0000,0000,0000,,And that's the same\Nthing as x plus 2.
Dialogue: 0,0:02:41.93,0:02:45.72,Default,,0000,0000,0000,,And, remember, it's 7 times\Nthe whole thing, x plus 1.
Dialogue: 0,0:02:45.72,0:02:47.79,Default,,0000,0000,0000,,So we actually have to use\Nthe distributive property.
Dialogue: 0,0:02:47.79,0:02:54.40,Default,,0000,0000,0000,,And that equals 7x plus 7.
Dialogue: 0,0:02:54.40,0:02:57.20,Default,,0000,0000,0000,,So now it's turned into a,\NI think this is a level
Dialogue: 0,0:02:57.20,0:02:58.79,Default,,0000,0000,0000,,three linear equation.
Dialogue: 0,0:02:58.79,0:03:02.05,Default,,0000,0000,0000,,And now all we do is, we say\Nwell let's get all the x's on
Dialogue: 0,0:03:02.05,0:03:02.96,Default,,0000,0000,0000,,one side of the equation.
Dialogue: 0,0:03:02.96,0:03:05.57,Default,,0000,0000,0000,,And let's get all the constant\Nterms, like the 2 and the 7, on
Dialogue: 0,0:03:05.57,0:03:07.10,Default,,0000,0000,0000,,the other side of the equation.
Dialogue: 0,0:03:07.10,0:03:08.89,Default,,0000,0000,0000,,So I'm going to choose to\Nget the x's on the left.
Dialogue: 0,0:03:08.89,0:03:10.99,Default,,0000,0000,0000,,So let's bring that\N7x onto the left.
Dialogue: 0,0:03:10.99,0:03:14.45,Default,,0000,0000,0000,,And we can do that by\Nsubtracting 7x from both sides.
Dialogue: 0,0:03:14.45,0:03:19.44,Default,,0000,0000,0000,,Minus 7x, plus,\Nit's a minus 7x.
Dialogue: 0,0:03:19.44,0:03:22.80,Default,,0000,0000,0000,,The right-hand side, these\Ntwo 7x's will cancel out.
Dialogue: 0,0:03:22.80,0:03:26.41,Default,,0000,0000,0000,,And on the left-hand side\Nwe have minus 7x plus x.
Dialogue: 0,0:03:26.41,0:03:32.84,Default,,0000,0000,0000,,Well, that's minus 6x plus\N2 is equal to, and on the
Dialogue: 0,0:03:32.84,0:03:35.08,Default,,0000,0000,0000,,right all we have left is 7.
Dialogue: 0,0:03:35.08,0:03:36.47,Default,,0000,0000,0000,,Now we just have to\Nget rid of this 2.
Dialogue: 0,0:03:36.47,0:03:41.36,Default,,0000,0000,0000,,And we can just do that by\Nsubtracting 2 from both sides.
Dialogue: 0,0:03:41.36,0:03:48.00,Default,,0000,0000,0000,,And we're left with minus\N6x packs is equal to 6.
Dialogue: 0,0:03:48.00,0:03:49.22,Default,,0000,0000,0000,,Now it's a level one problem.
Dialogue: 0,0:03:49.22,0:03:52.41,Default,,0000,0000,0000,,We just have to multiply both\Nsides times the reciprocal
Dialogue: 0,0:03:52.41,0:03:54.20,Default,,0000,0000,0000,,of the coefficient on\Nthe left-hand side.
Dialogue: 0,0:03:54.20,0:03:56.15,Default,,0000,0000,0000,,And the coefficient's\Nnegative 6.
Dialogue: 0,0:03:56.15,0:03:59.62,Default,,0000,0000,0000,,So we multiply both sides of\Nthe equation by negative 1/6.
Dialogue: 0,0:04:02.54,0:04:05.61,Default,,0000,0000,0000,,Negative 1/6.
Dialogue: 0,0:04:05.61,0:04:08.89,Default,,0000,0000,0000,,The left-hand side, negative\N1 over 6 times negative 6.
Dialogue: 0,0:04:08.89,0:04:10.19,Default,,0000,0000,0000,,Well that just equals 1.
Dialogue: 0,0:04:10.19,0:04:16.13,Default,,0000,0000,0000,,So we just get x is equal\Nto 5 times negative 1/6.
Dialogue: 0,0:04:16.13,0:04:19.25,Default,,0000,0000,0000,,Well, that's negative 5/6.
Dialogue: 0,0:04:22.27,0:04:23.21,Default,,0000,0000,0000,,And we're done.
Dialogue: 0,0:04:23.21,0:04:25.71,Default,,0000,0000,0000,,And if you wanted to check it,\Nyou could just take that x
Dialogue: 0,0:04:25.71,0:04:28.95,Default,,0000,0000,0000,,equals negative 5/6 and put it\Nback in the original question
Dialogue: 0,0:04:28.95,0:04:30.58,Default,,0000,0000,0000,,to confirm that it worked.
Dialogue: 0,0:04:30.58,0:04:31.34,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:04:34.61,0:04:37.94,Default,,0000,0000,0000,,I'm making these up on\Nthe fly, so I apologize.
Dialogue: 0,0:04:37.94,0:04:40.02,Default,,0000,0000,0000,,Let me think.
Dialogue: 0,0:04:40.02,0:04:51.01,Default,,0000,0000,0000,,3 times x plus 5 is equal\Nto 8 times x plus 2.
Dialogue: 0,0:04:51.01,0:04:52.74,Default,,0000,0000,0000,,Well, we do the\Nsame thing here.
Dialogue: 0,0:04:52.74,0:04:55.95,Default,,0000,0000,0000,,Although now we have two\Nexpressions we want to get
Dialogue: 0,0:04:55.95,0:04:56.68,Default,,0000,0000,0000,,out of the denominators.
Dialogue: 0,0:04:56.68,0:04:58.87,Default,,0000,0000,0000,,We want to get x plus 5\Nout and we want to get
Dialogue: 0,0:04:58.87,0:05:00.01,Default,,0000,0000,0000,,this x plus 2 out.
Dialogue: 0,0:05:00.01,0:05:01.67,Default,,0000,0000,0000,,So let's do the x plus 5 first.
Dialogue: 0,0:05:01.67,0:05:03.64,Default,,0000,0000,0000,,Well, just like we did before,\Nwe multiply both sides of
Dialogue: 0,0:05:03.64,0:05:05.57,Default,,0000,0000,0000,,this equation by x plus 5.
Dialogue: 0,0:05:05.57,0:05:07.63,Default,,0000,0000,0000,,You can say x plus 5 over 1.
Dialogue: 0,0:05:07.63,0:05:12.68,Default,,0000,0000,0000,,Times x plus 5 over 1.
Dialogue: 0,0:05:12.68,0:05:15.08,Default,,0000,0000,0000,,On the left-hand side,\Nthey get canceled out.
Dialogue: 0,0:05:15.08,0:05:24.23,Default,,0000,0000,0000,,So we're left with 3 is equal\Nto 8 times x plus five.
Dialogue: 0,0:05:24.23,0:05:28.77,Default,,0000,0000,0000,,All of that over x plus 2.
Dialogue: 0,0:05:28.77,0:05:31.82,Default,,0000,0000,0000,,Now, on the top, just to\Nsimplify, we once again
Dialogue: 0,0:05:31.82,0:05:34.42,Default,,0000,0000,0000,,just multiply the 8 times\Nthe whole expression.
Dialogue: 0,0:05:34.42,0:05:41.86,Default,,0000,0000,0000,,So it's 8x plus 40\Nover x plus 2.
Dialogue: 0,0:05:41.86,0:05:43.50,Default,,0000,0000,0000,,Now, we want to get\Nrid of this x plus 2.
Dialogue: 0,0:05:43.50,0:05:44.51,Default,,0000,0000,0000,,So we can do it the same way.
Dialogue: 0,0:05:44.51,0:05:46.50,Default,,0000,0000,0000,,We can multiply both sides\Nof this equation by
Dialogue: 0,0:05:46.50,0:05:50.90,Default,,0000,0000,0000,,x plus 2 over 1.
Dialogue: 0,0:05:50.90,0:05:52.58,Default,,0000,0000,0000,,x plus 2.
Dialogue: 0,0:05:52.58,0:05:53.69,Default,,0000,0000,0000,,We could just say we're\Nmultiplying both
Dialogue: 0,0:05:53.69,0:05:54.42,Default,,0000,0000,0000,,sides by x plus 2.
Dialogue: 0,0:05:54.42,0:05:56.63,Default,,0000,0000,0000,,The 1 is little unnecessary.
Dialogue: 0,0:05:56.63,0:06:02.91,Default,,0000,0000,0000,,So the left-hand side\Nbecomes 3x plus 6.
Dialogue: 0,0:06:02.91,0:06:05.07,Default,,0000,0000,0000,,Remember, always distribute\N3 times, because you're
Dialogue: 0,0:06:05.07,0:06:07.03,Default,,0000,0000,0000,,multiplying it times\Nthe whole expression.
Dialogue: 0,0:06:07.03,0:06:08.54,Default,,0000,0000,0000,,x plus 2.
Dialogue: 0,0:06:08.54,0:06:09.86,Default,,0000,0000,0000,,And on the right-hand side.
Dialogue: 0,0:06:09.86,0:06:13.62,Default,,0000,0000,0000,,Well, this x plus 2 and this\Nx plus 2 will cancel out.
Dialogue: 0,0:06:13.62,0:06:16.38,Default,,0000,0000,0000,,And we're left with 8x plus 40.
Dialogue: 0,0:06:16.38,0:06:19.34,Default,,0000,0000,0000,,And this is now a\Nlevel three problem.
Dialogue: 0,0:06:19.34,0:06:25.38,Default,,0000,0000,0000,,Well, if we subtract 8x from\Nboth sides, minus 8x, plus-- I
Dialogue: 0,0:06:25.38,0:06:26.97,Default,,0000,0000,0000,,think I'm running out of space.
Dialogue: 0,0:06:26.97,0:06:28.47,Default,,0000,0000,0000,,Minus 8x.
Dialogue: 0,0:06:28.47,0:06:31.29,Default,,0000,0000,0000,,Well, on the right-hand\Nside the 8x's cancel out.
Dialogue: 0,0:06:31.29,0:06:38.62,Default,,0000,0000,0000,,On the left-hand side we have\Nminus 5x plus 6 is equal
Dialogue: 0,0:06:38.62,0:06:42.32,Default,,0000,0000,0000,,to, on the right-hand side\Nall we have left is 40.
Dialogue: 0,0:06:42.32,0:06:45.38,Default,,0000,0000,0000,,Now we can subtract 6 from\Nboth sides of this equation.
Dialogue: 0,0:06:45.38,0:06:46.38,Default,,0000,0000,0000,,Let me just write out here.
Dialogue: 0,0:06:46.38,0:06:49.51,Default,,0000,0000,0000,,Minus 6 plus minus 6.
Dialogue: 0,0:06:49.51,0:06:51.47,Default,,0000,0000,0000,,Now I'm going to, hope I\Ndon't lose you guys by
Dialogue: 0,0:06:51.47,0:06:53.16,Default,,0000,0000,0000,,trying to go up here.
Dialogue: 0,0:06:55.72,0:06:58.41,Default,,0000,0000,0000,,But if we subtract minus 6 from\Nboth sides, on the left-hand
Dialogue: 0,0:06:58.41,0:07:05.28,Default,,0000,0000,0000,,side we're just left with\Nminus 5x equals, and on the
Dialogue: 0,0:07:05.28,0:07:08.78,Default,,0000,0000,0000,,right-hand side we have 34.
Dialogue: 0,0:07:08.78,0:07:09.88,Default,,0000,0000,0000,,Now it's a level one problem.
Dialogue: 0,0:07:09.88,0:07:12.78,Default,,0000,0000,0000,,We just multiply both\Nsides times negative 1/5.
Dialogue: 0,0:07:16.51,0:07:18.36,Default,,0000,0000,0000,,Negative 1/5.
Dialogue: 0,0:07:18.36,0:07:21.13,Default,,0000,0000,0000,,On the left-hand\Nside we have x.
Dialogue: 0,0:07:21.13,0:07:27.13,Default,,0000,0000,0000,,And on the right-hand side\Nwe have negative 34/5.
Dialogue: 0,0:07:27.13,0:07:29.64,Default,,0000,0000,0000,,Unless I made some careless\Nmistakes, I think that's right.
Dialogue: 0,0:07:29.64,0:07:33.19,Default,,0000,0000,0000,,And I think if you understood\Nwhat we just did here, you're
Dialogue: 0,0:07:33.19,0:07:36.78,Default,,0000,0000,0000,,ready to tackle some level\Nfour linear equations.
Dialogue: 0,0:07:36.78,0:07:38.29,Default,,0000,0000,0000,,Have fun.