Solving Inequalities with Addition or Subtraction - Free Educational videos for Students in K-12

Solving Inequalities with Addition or Subtraction - By Anywhere Math

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00:0-1	Welcome to anywhere Math . I'm Jeff Jacobson . And
00:02	today we're gonna talk about solving inequalities using addition and
00:06	subtraction . Let's get started . Mhm . All right
00:26	, let's get right into our first example , solve
00:29	x minus 2.7 is less than negative five . And
00:34	graft a solution . So first when you're solving inequalities
00:39	, it's just like solving an equation . The only
00:41	difference is uh you've got this inequality symbol instead of
00:45	an equal sign . But you go about it the
00:47	same way you try to get the variable alone on
00:51	one side and then whatever value on the other side
00:53	. Okay ? So uh if you see we've got
00:56	X -2.7 is less than -5 . Again my goal
01:03	, I'm trying to get this variable X alone .
01:06	So I'm going to concentrate over here . I've got
01:09	X -2.7 . So to get rid of the 2.7
01:13	this -2.7 , I'm going to add 2.7 . I
01:16	do the opposite . If I add 2.7 to this
01:20	side , I do the same here Plus 2.7 .
01:25	Right , well those are gonna cancel out . I
01:29	have X . Bring down the less than is less
01:33	than negative five plus 2.7 . I've got a negative
01:37	and a positive . So something's cancelling out 2.7 is
01:40	canceling out . I've got 2.3 and because the negative
01:45	five the absolute value of it is greater . That
01:48	means that's gonna be negative . Uh so this is
01:51	my solution X is less than negative 2.3 . If
01:56	I want to check that , all I have to
01:59	do is Pick a number for X . That's less
02:02	than negative 2.3 and substituted in . So maybe I'll
02:06	say , okay well What if X is -3 ,
02:11	-3 is less than negative 2.3 . So if I
02:15	substitute that in for my check I would have negative
02:22	three -2.7 . And the question is that this is
02:29	our check Less than -5 . Well negative three minus
02:34	uh 2.7 is negative five .7 which in fact is
02:41	less than -5 . It's farther to the left on
02:44	the number line , Uh farther negative so it is
02:48	less than -5 . Uh Which means that's great .
02:52	We're good . Now my second part I have to
02:55	graft that solution so that's pretty simple . Start off
03:00	with a number line and I don't really mind .
03:08	It doesn't have to be super fancy . Uh X
03:10	is less than negative 2.3 . I'm gonna put a
03:13	zero here , -2.3 is going to be down here
03:17	, assist their negative 2.3 . I'm not really concerned
03:21	with a whole bunch of marks and numbers laid out
03:24	. I just I like to put the zero there
03:27	and negative 2.3 . Now what I do need to
03:29	look at is the symbol that's less than . Which
03:32	means it does not include -2.3 . So on my
03:36	graph I need to put an open circle open dot
03:41	. That means it does not include -2.3 . So
03:44	that's really important if it was less than or equal
03:47	to than it would . Uh X is less than
03:50	that . So I'm gonna draw my arrow going to
03:53	the left less than here's some to try on your
03:56	own example to solve 13 is less than or equal
04:11	to X plus 14 and then grafted solution . So
04:15	same thing I'm going to try to get the variable
04:17	alone 13 is less than or equal to X plus
04:22	14 . So I'm looking over here that's what I'm
04:25	concentrating . X is not alone , we're adding 14
04:30	to it . So to get rid of that plus
04:32	14 I do the opposite . I subtract 14 ,
04:36	Write anything I do to one side due to the
04:39	other -14 . Here that goes away . I'm left
04:45	with X alone which is my goal on the right
04:49	, I still have The less than or equal to
04:52	and 13 -14 would give me -1 . Now to
04:56	check , all I have to do again is if
05:03	I'm saying X is going to be greater than or
05:06	equal to negative one , just pick a number in
05:09	that solution . Uh Let's say well zero Is greater
05:13	than or equal to -1 . So let's check zero
05:16	. So my question is yeah is zero plus 14
05:23	Gonna be greater than or equal to 13 or again
05:29	? Mhm . Is 13 less than or equal to
05:31	14 ? Yes of course it is . So that
05:35	works for my solution so now I'm gonna go and
05:40	how my number line got the solution so the same
05:44	thing doesn't have to be super fancy . Uh I'll
05:49	start with zero there ex at -1 . Now here
05:55	you gotta be careful . Uh it's less than or
05:58	equal to so that's going to be a closed dot
06:03	and now this might be a little bit tricky because
06:06	you're thinking okay now I'll send the variables on the
06:09	right side . I've got negative one is less than
06:11	or equal to X . Which means if I if
06:15	I want to rewrite it I can't if I read
06:18	it from right to left which is kind of you
06:21	typically read the variable first that would be X .
06:25	Is greater than or equal to negative one . And
06:31	that might be a little bit easier for when you
06:33	need to graph . These are the same , so
06:36	feel free to write it either way . Uh And
06:38	if you want to rewrite it like that , then
06:40	that might help you uh when your graphing , So
06:43	X is greater than or equal to -1 . Here's
06:47	negative one or equal to so close dot greater than
06:51	or equal to . So I'm going up and to
06:54	the right , okay , here's some more to try
06:56	on your own . All right , Here's our last
07:09	example . A person can be no taller than 6.25
07:13	ft to become an astronaut for NASA . I guess
07:16	you got to be able to fit inside the space
07:19	shuttle . Uh Your friend is five ft nine inches
07:22	tall . Right ? And solve an inequality that represents
07:26	how much your friend can still grow , can still
07:29	grow and become an astronaut . Um So looking at
07:33	this word problem , if you want to pause it
07:35	and see if you can figure this out yourself ,
07:37	go for it . Uh First we're going to look
07:40	for some kind of key words . Hopefully , you
07:43	know , it's a person can be no taller than
07:46	Well , that's very important . That's kind of why
07:48	we're going to be writing an inequality and not an
07:51	equation . Uh 6.25 ft is important to become an
07:56	astronaut for NASA , your friend is 5' 9" tall
08:00	. That's important . Uh and then obviously we got
08:03	to write and solve our inequalities . Uh First hopefully
08:07	you notice we've got 6.25 ft and then we've got
08:11	five ft nine inches . This is written in just
08:14	feet with decimal , this is with feet and inches
08:17	. So that's a problem . Right off the bat
08:20	, I need to make this look like that ,
08:23	so I need five ft nine inches as a decimal
08:26	in just feet . So the question is , well
08:28	nine inches is how much of a foot nine inches
08:33	is nine out of 12 ? Right ? Because there's
08:38	12" in a foot . Uh if I simplify that
08:41	, that's gonna be 3/4 And 3/4 as a decimal
08:47	, hopefully you know that is 0.75 . So That
08:54	helps . five ft 9" tall would then be equal
08:58	to 5.75 feet . Okay , so that's nice .
09:04	Now we've got two decimals . Uh , the units
09:06	we're using is just feet . Now I need to
09:09	write and solve my inequality . Well what is going
09:15	to be my variable ? Right , I'm making this
09:18	inequality , I'm going to have a variable right ?
09:20	And solve an inequality represents how much your friend can
09:23	still grow . That is what we don't know .
09:28	And usually in these word problems when there's something you
09:31	don't know and you have to write an expression or
09:34	an equation or in this case in inequality , whatever
09:37	that thing you don't know is that usually is going
09:39	to be your variable , so how much your friend
09:42	can still grow ? Let's call that . How about
09:46	G . For growth ? Okay so that's going to
09:49	be represented by G . Um This is where our
09:53	friend is starting at , So 5.75 , How much
10:00	they can still grow ? We would add that .
10:02	So plus G . That's what we decided what we're
10:06	gonna call , how much you can still grow ?
10:07	5.75 plus G . Now 6.25 ft . You can't
10:13	be taller than that , no taller than . Can
10:17	you be 6.25 ft ? Yeah you can be that
10:21	or less . That's the maximum no taller than that
10:25	. So how would I write that ? What symbol
10:28	? What inequality symbol would I use ? Well I
10:31	can't be taller than that . That's the max .
10:33	So I have to be that or less . So
10:36	that's going to be less than or equal to 6.25
10:44	. So again this is how tall my friend is
10:47	right now . How much he can grow is plus
10:51	G . Right ? If you grew an inch Uh
10:54	he would be 6.75 which is too tall . Right
10:58	? So he can't do that . Um But he
11:01	has to be less than or equal to 6.25 .
11:03	That's the max . He can't be more than that
11:06	. So there's my inequality . I did the first
11:08	part . Right ? And inequality now I need to
11:11	solve it . Well to solve we know how to
11:14	do this . I want to get the variable alone
11:17	right now I have this uh positive 5.75 . So
11:20	to solve it I'm going to subtract -5.75 to both
11:27	sides . Mhm . And that's gonna cancel that .
11:33	I'm gonna be left with G . Is less than
11:36	or equal to . Hopefully you can't see that .
11:40	Let me write it over here . So I'm gonna
11:42	get G . is less than or equal to uh
11:49	five Too . Sorry 6.25 -5.75 . When I do
11:54	that subtraction uh I'm gonna get zero point five .
12:01	So in words what we would say is your friend
12:04	can grow no more than 0.5 ft . Or if
12:13	we want to write that in inches or six inches
12:17	Frank can grow more than 6" and still be an
12:20	astronaut . Here's some more to try on your own
12:31	. Thanks so much for watching and if you like
12:33	this video please subscribe . Mhm .

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