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Dialogue: 0,0:00:00.04,0:00:04.04,Default,,0000,0000,0000,,Welcome to the presentation on solving inequalities
Dialogue: 0,0:00:04.04,0:00:07.00,Default,,0000,0000,0000,,or I guess you could call them\Nalgebraic inequalities.
Dialogue: 0,0:00:07.00,0:00:09.02,Default,,0000,0000,0000,,So let's get started.
Dialogue: 0,0:00:09.03,0:00:12.05,Default,,0000,0000,0000,,If I were to tell you\Nthat, well, let's just say
Dialogue: 0,0:00:12.05,0:00:17.09,Default,,0000,0000,0000,,x > 5, right?
Dialogue: 0,0:00:18.00,0:00:22.08,Default,,0000,0000,0000,,So x could be 5.01, it could be 5.5,\Nit could be a million.
Dialogue: 0,0:00:22.09,0:00:26.03,Default,,0000,0000,0000,,It just can't be 4 or 3\Nor 0 or -8.
Dialogue: 0,0:00:26.04,0:00:28.01,Default,,0000,0000,0000,,And actually,\Njust for convenience,
Dialogue: 0,0:00:28.02,0:00:31.00,Default,,0000,0000,0000,,let's actually draw\Nthat on the number line.
Dialogue: 0,0:00:31.01,0:00:33.03,Default,,0000,0000,0000,,That's the number line.
Dialogue: 0,0:00:33.03,0:00:36.09,Default,,0000,0000,0000,,And if this is 5,\Nx can't be equal to 5
Dialogue: 0,0:00:37.00,0:00:39.09,Default,,0000,0000,0000,,so we draw a big circle here\Nand then we would color
Dialogue: 0,0:00:40.00,0:00:42.01,Default,,0000,0000,0000,,in all the values\Nthat x could be.
Dialogue: 0,0:00:42.02,0:00:45.08,Default,,0000,0000,0000,,So x could be 5.000001,
Dialogue: 0,0:00:45.09,0:00:48.06,Default,,0000,0000,0000,,it just has to be\Na little bit bigger than 5
Dialogue: 0,0:00:48.07,0:00:50.09,Default,,0000,0000,0000,,and any of those\Nwould satisfy, right?
Dialogue: 0,0:00:51.00,0:00:53.06,Default,,0000,0000,0000,,So let's just write\Nsome numbers that satisfy.
Dialogue: 0,0:00:53.07,0:00:56.01,Default,,0000,0000,0000,,6 would satisfy it,\N10 would satisfy it,
Dialogue: 0,0:00:56.02,0:00:57.09,Default,,0000,0000,0000,,100 would satisfy it.
Dialogue: 0,0:00:58.00,0:01:01.00,Default,,0000,0000,0000,,Now, if I were to multiply\Nor, I guess, divide,
Dialogue: 0,0:01:01.01,0:01:03.08,Default,,0000,0000,0000,,both sides of this,\NI guess we could say equation,
Dialogue: 0,0:01:03.09,0:01:09.08,Default,,0000,0000,0000,,or this inequality, by -1,\NI wanna understand what happens.
Dialogue: 0,0:01:09.09,0:01:15.09,Default,,0000,0000,0000,,So what's the relation\Nbetween -x and -5?
Dialogue: 0,0:01:17.04,0:01:19.00,Default,,0000,0000,0000,,And when I say,\Nwhat's the relation,
Dialogue: 0,0:01:19.00,0:01:24.03,Default,,0000,0000,0000,,is it greater than\Nor is it less than -5?
Dialogue: 0,0:01:24.03,0:01:27.72,Default,,0000,0000,0000,,Well, 6 is a value\Nthat works for x,
Dialogue: 0,0:01:27.72,0:01:33.03,Default,,0000,0000,0000,,so -6, is that greater than\Nor less than -5?
Dialogue: 0,0:01:33.03,0:01:36.09,Default,,0000,0000,0000,,-6 is less than -5, right?
Dialogue: 0,0:01:37.00,0:01:41.01,Default,,0000,0000,0000,,So let me draw\Nthe number line here.
Dialogue: 0,0:01:41.01,0:01:44.04,Default,,0000,0000,0000,,If we have -5 here--\Nlet's just draw a circle around it
Dialogue: 0,0:01:44.05,0:01:46.07,Default,,0000,0000,0000,,because we know\Nit's not gonna equal to -5
Dialogue: 0,0:01:46.08,0:01:48.05,Default,,0000,0000,0000,,because we're just deciding
Dialogue: 0,0:01:48.06,0:01:50.01,Default,,0000,0000,0000,,between greater than\Nor less than.
Dialogue: 0,0:01:50.02,0:01:54.04,Default,,0000,0000,0000,,So we're saying 6 works\Nfor x, so -6 is here, right?
Dialogue: 0,0:01:54.04,0:01:56.04,Default,,0000,0000,0000,,-6.
Dialogue: 0,0:01:56.04,0:01:58.61,Default,,0000,0000,0000,,So -6 is less than -5
Dialogue: 0,0:01:58.61,0:02:03.02,Default,,0000,0000,0000,,So is -10, so is -100, so is -1,000,000, right?
Dialogue: 0,0:02:03.02,0:02:08.10,Default,,0000,0000,0000,,So, turns out -X is less than -5
Dialogue: 0,0:02:08.10,0:02:11.33,Default,,0000,0000,0000,,So this is really all you have to remember
Dialogue: 0,0:02:11.33,0:02:14.44,Default,,0000,0000,0000,,When you are working with inequalities in algebra
Dialogue: 0,0:02:14.44,0:02:18.20,Default,,0000,0000,0000,,Inequalities you can treat them just the way
Dialogue: 0,0:02:18.20,0:02:21.10,Default,,0000,0000,0000,,A > or a < sign you can treat them just the way you would treat an = sign
Dialogue: 0,0:02:21.10,0:02:24.75,Default,,0000,0000,0000,,The only difference is: if you multiply or divide
Dialogue: 0,0:02:24.75,0:02:29.82,Default,,0000,0000,0000,,both sides of the equation by a negative number
Dialogue: 0,0:02:29.82,0:02:30.65,Default,,0000,0000,0000,,You swap it
Dialogue: 0,0:02:30.65,0:02:31.77,Default,,0000,0000,0000,,That's all you have to remember
Dialogue: 0,0:02:31.78,0:02:34.32,Default,,0000,0000,0000,,Let's do some problems and hopefully that will bring the point home
Dialogue: 0,0:02:34.32,0:02:38.06,Default,,0000,0000,0000,,If you ever forget, you just have to try, you just have to remember this
Dialogue: 0,0:02:38.06,0:02:41.28,Default,,0000,0000,0000,,X is > 5, well then -X < -5
Dialogue: 0,0:02:41.28,0:02:42.24,Default,,0000,0000,0000,,And keep trying out numbers
Dialogue: 0,0:02:42.24,0:02:45.52,Default,,0000,0000,0000,,That's what is going to give you the best intuition
Dialogue: 0,0:02:45.52,0:02:46.94,Default,,0000,0000,0000,,Let's do some problems
Dialogue: 0,0:02:46.94,0:02:56.14,Default,,0000,0000,0000,,So if I say that 3X + 2 is less than or equal to 1
Dialogue: 0,0:02:56.14,0:02:58.08,Default,,0000,0000,0000,,Well, this is a pretty easy equation to solve
Dialogue: 0,0:02:58.08,0:03:01.40,Default,,0000,0000,0000,,We say 3X, let's subtract 2 from both sides
Dialogue: 0,0:03:01.40,0:03:03.10,Default,,0000,0000,0000,,When you do add or subtract
Dialogue: 0,0:03:03.10,0:03:04.88,Default,,0000,0000,0000,,You don't do anything to the inequality
Dialogue: 0,0:03:04.88,0:03:07.66,Default,,0000,0000,0000,,So if you subtract 2 from both sides
Dialogue: 0,0:03:07.66,0:03:12.45,Default,,0000,0000,0000,,You get 3X is less than or equal to -1, right?
Dialogue: 0,0:03:12.45,0:03:16.53,Default,,0000,0000,0000,,And then now we are going to divide both sides by 3
Dialogue: 0,0:03:16.53,0:03:22.29,Default,,0000,0000,0000,,We get X is less than or equal to -1/3
Dialogue: 0,0:03:22.29,0:03:24.01,Default,,0000,0000,0000,,Look we didn't change anything
Dialogue: 0,0:03:24.01,0:03:26.70,Default,,0000,0000,0000,,Because we divided both sides by a positive 3
Dialogue: 0,0:03:26.70,0:03:31.95,Default,,0000,0000,0000,,Alright? We could have done this equation in a slightly different way
Dialogue: 0,0:03:31.95,0:03:35.44,Default,,0000,0000,0000,,What if we subtracted 1 from both sides
Dialogue: 0,0:03:35.44,0:03:37.58,Default,,0000,0000,0000,,So this is another way of solving it
Dialogue: 0,0:03:37.58,0:03:42.39,Default,,0000,0000,0000,,What if we said 3X + 1 is equal to or less than 0
Dialogue: 0,0:03:42.39,0:03:44.46,Default,,0000,0000,0000,,I just subtracted 1 from both sides
Dialogue: 0,0:03:44.46,0:03:46.64,Default,,0000,0000,0000,,And now I'll subtract 3X from both sides
Dialogue: 0,0:03:46.64,0:03:51.46,Default,,0000,0000,0000,,I'll get 1 is less than or equal to -3X
Dialogue: 0,0:03:51.46,0:03:53.48,Default,,0000,0000,0000,,I subtracted 3X from here
Dialogue: 0,0:03:53.48,0:03:54.78,Default,,0000,0000,0000,,So I'll subtract 3X from here
Dialogue: 0,0:03:54.78,0:03:58.26,Default,,0000,0000,0000,,Now I'll have to divide both sides by a negative number
Dialogue: 0,0:03:58.26,0:04:02.35,Default,,0000,0000,0000,,Right? Because I'm going to divide both sides by -3
Dialogue: 0,0:04:02.35,0:04:05.47,Default,,0000,0000,0000,,So I get -1/3 on this side
Dialogue: 0,0:04:05.47,0:04:07.25,Default,,0000,0000,0000,,And based on what we had just learned
Dialogue: 0,0:04:07.27,0:04:08.48,Default,,0000,0000,0000,,Since we are dividing by a negative number
Dialogue: 0,0:04:08.48,0:04:10.26,Default,,0000,0000,0000,,We want to swap the inequality right?
Dialogue: 0,0:04:10.26,0:04:11.78,Default,,0000,0000,0000,,It was less than or equal to
Dialogue: 0,0:04:11.78,0:04:15.16,Default,,0000,0000,0000,,And it's going to be greater than or equal to X
Dialogue: 0,0:04:15.16,0:04:19.18,Default,,0000,0000,0000,,Now did we get the same answer when did both in two different ways?
Dialogue: 0,0:04:22.57,0:04:25.92,Default,,0000,0000,0000,,And here we got -1/3 is greater than or equal to X
Dialogue: 0,0:04:19.18,0:04:22.57,Default,,0000,0000,0000,,Here we got X is less than or equal to negative 1/3
Dialogue: 0,0:04:25.92,0:04:27.40,Default,,0000,0000,0000,,That's the same answer right?
Dialogue: 0,0:04:27.40,0:04:29.58,Default,,0000,0000,0000,,X is less than or equal to negative 1/3
Dialogue: 0,0:04:29.58,0:04:31.96,Default,,0000,0000,0000,,That's what I find to be the cool thing about algebra.
Dialogue: 0,0:04:31.96,0:04:33.96,Default,,0000,0000,0000,,You can tackle a problem in a bunch of two different ways.
Dialogue: 0,0:04:33.96,0:04:37.56,Default,,0000,0000,0000,,You should get the right answer as long as I guess you do it right.
Dialogue: 0,0:04:37.56,0:04:41.89,Default,,0000,0000,0000,,Let's do a couple more problems.
Dialogue: 0,0:04:41.89,0:04:46.86,Default,,0000,0000,0000,,Erase the thing. Here you go. Let's do a slightly harder one.
Dialogue: 0,0:04:46.86,0:04:56.75,Default,,0000,0000,0000,,Let's say - 8x + 7 > 5x +2
Dialogue: 0,0:04:56.75,0:05:02.14,Default,,0000,0000,0000,,Let's subtract 5x from both sides.
Dialogue: 0,0:05:02.14,0:05:06.08,Default,,0000,0000,0000,,- 13x + 7 > 2
Dialogue: 0,0:05:06.08,0:05:09.75,Default,,0000,0000,0000,,Now we can subtract 7\Nfrom both sides,
Dialogue: 0,0:05:09.75,0:05:13.47,Default,,0000,0000,0000,,-13x > -5.
Dialogue: 0,0:05:13.47,0:05:17.31,Default,,0000,0000,0000,,Now we're gonna divide both\Nsides of this equation by -13.
Dialogue: 0,0:05:17.31,0:05:19.46,Default,,0000,0000,0000,,Well, very easy.
Dialogue: 0,0:05:19.46,0:05:24.94,Default,,0000,0000,0000,,It's just x, and on this side\N-5/-13 = 5/13, right?
Dialogue: 0,0:05:24.94,0:05:26.70,Default,,0000,0000,0000,,The negatives cancel out.
Dialogue: 0,0:05:26.70,0:05:30.07,Default,,0000,0000,0000,,And since we divided\Nby a negative,
Dialogue: 0,0:05:30.07,0:05:31.85,Default,,0000,0000,0000,,we switch the sign.
Dialogue: 0,0:05:31.85,0:05:34.29,Default,,0000,0000,0000,,x is less than 5/13
Dialogue: 0,0:05:34.29,0:05:35.72,Default,,0000,0000,0000,,And once again,\Njust like the beginning,
Dialogue: 0,0:05:35.72,0:05:37.97,Default,,0000,0000,0000,,if you don't believe me,\Ntry out some numbers.
Dialogue: 0,0:05:37.97,0:05:39.08,Default,,0000,0000,0000,,I remember\Nwhen I first learned this
Dialogue: 0,0:05:39.08,0:05:40.73,Default,,0000,0000,0000,,I didn't believe the teacher\Nso I did try out numbers
Dialogue: 0,0:05:40.75,0:05:44.54,Default,,0000,0000,0000,,and that's how I got convinced\Nthat it works
Dialogue: 0,0:05:44.54,0:05:47.05,Default,,0000,0000,0000,,when you multiply or divide\Nboth sides of this equation
Dialogue: 0,0:05:47.05,0:05:50.22,Default,,0000,0000,0000,,by a negative sign,\Nyou swap the inequality.
Dialogue: 0,0:05:50.22,0:05:53.04,Default,,0000,0000,0000,,And remember: that's only\Nwhen you multiply or divide,
Dialogue: 0,0:05:53.05,0:05:55.78,Default,,0000,0000,0000,,not when you add or subtract.
Dialogue: 0,0:05:55.78,0:05:57.66,Default,,0000,0000,0000,,I think that should give you
Dialogue: 0,0:05:57.66,0:05:59.81,Default,,0000,0000,0000,,a good idea of how to do\Nthese problems.
Dialogue: 0,0:05:59.81,0:06:01.08,Default,,0000,0000,0000,,There's really\Nnot much new here.
Dialogue: 0,0:06:01.08,0:06:05.29,Default,,0000,0000,0000,,You do an inequality or--\NI guess you could call this
Dialogue: 0,0:06:05.29,0:06:08.00,Default,,0000,0000,0000,,an inequality equation--\Nyou do it exactly the same way
Dialogue: 0,0:06:08.01,0:06:10.08,Default,,0000,0000,0000,,you would do\Na normal linear equation.
Dialogue: 0,0:06:10.08,0:06:14.48,Default,,0000,0000,0000,,The only difference being is\Nif you multiply or you divide
Dialogue: 0,0:06:14.48,0:06:16.03,Default,,0000,0000,0000,,both sides of the equation\Nby a negative number,
Dialogue: 0,0:06:16.04,0:06:19.26,Default,,0000,0000,0000,,then you swap the inequality.
Dialogue: 0,0:06:19.26,0:06:22.05,Default,,0000,0000,0000,,I think you're ready now\Nto try some practice problems.
Dialogue: 0,0:06:22.06,0:06:24.04,Default,,0000,0000,0000,,Have fun.