Solving Equations Using Addition or Subtraction - Free Educational videos for Students in K-12

Solving Equations Using Addition or Subtraction - By Anywhere Math

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00:0-1	Welcome anywhere Math . I'm Jeff Jacobson . And today
00:03	today is a very exciting day . We're going to
00:05	get into a little bit of algebra with solving equations
00:08	using addition and subtraction . Let's get started . Mhm
00:29	. All right . Here's our first example . Tell
00:31	whether the given value is the solution to the equation
00:35	. Now , before we get started , we've got
00:37	a new term here solution . Uh So what exactly
00:42	is a solution ? Well , a solution to an
00:44	equation is just the value for a variable . That
00:48	makes the equation true . Okay , now with an
00:51	equation you have , one side is equal to another
00:55	side . So for it to be true , that
00:58	has to stay true . Right , This site has
01:00	to be equal to this side . If they're not
01:03	equal then it's not an equation . Okay . And
01:06	that would not be a solution . So let's see
01:09	with the first one for a P plus 10 is
01:12	equal to 38 if p is 18 . So we're
01:15	trying to see if 18 is a solution to this
01:19	equation . So to figure that out . All we
01:21	do is substitute . Were saying P . Is equal
01:24	to 18 . So then I'm gonna substitute 18 and
01:27	for P . So I get 18 . I'll just
01:31	do that in a different color . Uh Plus 10
01:34	is equal to 38 . Well 18 plus 10 Is
01:40	28 which is not equal to 38 . Now the
01:46	fact that those are not equal means that 18 is
01:49	not a solution , not a solution . Okay Because
01:59	this equation is not true right ? When 18 is
02:01	is for p . Okay let's do the next 14
02:05	Y equals 56 . Why is equal to 14 ?
02:08	So again we're seeing at 14 is a solution for
02:11	why for this equation ? So we're gonna substitute .
02:14	So it's just gonna be four times 14 . Using
02:20	my presence is when uh substitute is equal to 56
02:25	. Well four times 14 is 56 . That's equal
02:29	to 56 which means yes , 14 is a solution
02:34	. Mhm . Mhm . Mhm . Okay , so
02:39	14 is a solution . Ah Here's something try on
02:42	your own . Okay . Next , before we get
02:52	into example , number two , I want to talk
02:54	a little bit about equations . Now . You should
02:57	know an equation has an equal sign where one side
03:00	is equal to another side is different than an expression
03:03	. Um But let's talk a little bit more about
03:06	that . A really good way to uh give an
03:09	example of equations is with a scale , right Scale
03:13	has one side equal to another . If they're not
03:16	equal , the scale is gonna show that and they
03:18	will it will kind of tilt like that . So
03:21	here's an example . I've got this red ball plus
03:25	three little blue blocks and then on the other side
03:29	I've got 73 and four more is seven blue blocks
03:33	. Um And you can see in the scale it's
03:35	balanced , which means this side the weight of this
03:39	side is equal to the weight of that side .
03:41	That's why it's balanced . Now , if I want
03:45	to figure out , well , how much does that
03:47	red ball way ? Well , um one thing I
03:51	could do , I if I took one of these
03:54	blocks away , well if I did that to one
03:59	side , then all of a sudden this they were
04:03	balanced , I took one away , so now that's
04:05	going to be a little bit lighter than this side
04:07	, right ? So that would go up . Um
04:09	But equations , I wanted to be equal this set
04:12	equal to this side , so if I took one
04:13	away here , if I also took one away here
04:18	, well then it was later , but now it's
04:20	going to balance out again , I could take away
04:24	the same amount from each side and will stay balanced
04:26	. I could also add if I put another blue
04:29	block back on their one on each side , it
04:31	would stay balanced again . Now if I'm trying to
04:36	find exactly how much the red ball weighs , you
04:40	might think , well , I'm gonna have to get
04:42	the red ball balanced with something on this side .
04:45	Just the red ball , right , that would tell
04:48	me how much it weighs . Well , I took
04:50	one away from here and one away from here and
04:52	it stayed balanced . So I could also take two
04:55	more away from here . If I take those two
04:59	away now I've got the red ball all by itself
05:05	, but again , if I took those away it's
05:07	going to be lighter here . I want to make
05:08	sure it stays balanced . So I got to do
05:10	the same thing to this side and I can take
05:14	those two away . So doing that . Now ,
05:21	hopefully you can see well , how much does that
05:24	red ball way ? Well , the red ball is
05:27	equal to four of those blue blocks . Okay ,
05:31	that's exactly what we're doing uh with solving equations .
05:36	Okay , we're basically trying to get The variable alone
05:42	on one side equal to something on the other side
05:45	. Okay , when we achieve that , then we
05:47	basically have found our solution . Okay , let's look
05:50	at example , All right , here's example , number
05:53	two , solve X minus two is equal to six
05:57	solving an equation . Just means finding the solution .
06:01	Okay , So I'm trying to find the solution that
06:03	would make this equation true . What value of X
06:06	would make this equation true ? Um Now it's gonna
06:10	be pretty simple . And the problems that the beginning
06:13	will be pretty simple . A lot of them ,
06:14	you'll be able to figure out just on your own
06:17	using mental math . But that's not the point .
06:19	The point is to learn the process so that when
06:22	it gets more difficult , when you have very difficult
06:25	equations to solve , you already know what to do
06:29	. You know the steps to take to get your
06:31	solution . So just trust me , follow the ,
06:34	follow the steps , learn uh learn how to solve
06:39	these equations with easy ones . So then when it
06:41	gets more difficult you'll know what to do . Um
06:44	So again , the goal I think of the scale
06:48	problem , the goal , I was trying to get
06:50	the red ball all by itself with something else ,
06:53	everything else on the other side and have it equal
06:56	. Okay , same thing here , I need to
06:58	get the variable alone . That's the goal when uh
07:01	when solving equations right now it's been subtracted by two
07:06	. Well , to undo that's subtraction , I use
07:10	the inverse operations . The opposite of subtraction is addition
07:15	. So if I add two , That -2 will
07:19	go away , you can think of it . Well
07:21	what if you had 10 -2 plus two ? This
07:25	-2-plus 2 . Those are opposites . Those are Subtraction
07:30	and addition are are inverse operations are opposite in operations
07:35	. So they would cancel each other out that that
07:37	would become zero and I'm just left with 10 .
07:40	So same thing here instead of the 10 though it's
07:43	an X . So if I add to that goes
07:46	away and I have X alone . But remember on
07:50	the scale problem when I took two blocks away from
07:54	one side , if I just did that , it
07:57	would become unbalanced . The most important thing with solving
08:01	equations is that anything I do to one side ,
08:04	I do the exact same thing to the other side
08:07	, the other side of the , of the equal
08:09	side . So when I took two blocks away from
08:12	here , I also took two blocks away from here
08:14	so that it stayed balanced . Same thing here .
08:17	If I add two on this left side , I
08:20	add to on this right side . Okay , so
08:24	those go away , I'm left with X . Bring
08:28	down my equal sign , and six plus two is
08:30	eight . Okay , so to check to see if
08:34	that is my solution , all I have to do
08:36	is substitute it back in . You should never miss
08:39	uh an equations problem , right ? Because you can
08:42	always check , you can always check your answer .
08:44	So substitute eight back in while 8 -2 . Is
08:48	that six ? Yes , it is . So okay
08:52	, eight is my solution . Okay , let's try
08:54	another one . So how about um 18 Equals X
09:02	-7 . Okay , now it looks a little bit
09:06	different because now the variables on the right side ,
09:08	but it doesn't matter , it doesn't matter which side
09:11	it's on , The process is the same . So
09:13	again , my whole goal is to get the variable
09:16	alone . So I'm going to focus on this side
09:18	first . I don't even care over here , X
09:22	-7 . Well to undo that -7 or to get
09:26	rid of it , I need to do the opposite
09:29	. I'm going to add seven and the most important
09:32	kind of the golden rule , anything I do to
09:34	one side , I do the exact same thing to
09:37	the other to make sure it stays balance . So
09:39	I add seven here , those go away , I'm
09:43	left with X is equal to 25 . And if
09:48	I want to check to see if that's a solution
09:51	Subsequuted back in 25 -7 is 18 . So yeah
09:58	, I'm happy with that . That's my solution .
10:00	Here's some more to try on your own . All
10:08	right , here's our last example solve X plus 13
10:12	is equal to 27 . Going about it the same
10:15	way focusing on the side that's got the variable .
10:18	My goal is to get that variable alone . So
10:21	right now we've got we're adding 13 to it so
10:24	I need to get rid of that . Plus 13
10:26	inverse operations of addition is subtraction . So I am
10:30	going to subtract 13 . Anything I do to one
10:35	side . I do the exact same thing to the
10:37	other . Subtract 13 . Here that goes away ,
10:42	I'm left with X . Bring down my equal sign
10:44	, 27 minus 13 is 14 and before I'm gonna
10:49	box my answer , I'm gonna check by substituting it
10:53	back in uh for X . So 14 plus 13
10:57	, is that 27 ? Yes , it is .
10:59	So 14 is my solution . Here's some more to
11:03	try on your own . Thank you so much for
11:12	watching , and if you like this video , please
11:13	subscribe . Mhm .

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