How To Solve Linear Equations In Algebra - Free Educational videos for Students in K-12

How To Solve Linear Equations In Algebra - By The Organic Chemistry Tutor

Transcript


00:00	in this video , we're going to focus on solving
00:03	linear equations . So let's begin with this example ,
00:07	X plus four Is equal to seven . How can
00:12	we solve this linear equation ? The goal here is
00:19	to calculate the value of X . Now you might
00:22	be wondering what is X . X is a variable
00:26	? It has a value that we currently don't know
00:29	and X is just basically a number . We just
00:31	got to find out the value of that number .
00:34	So now let's think about this equation intuitively What number
00:39	Plus four Is equal to seven . If you think
00:44	about it , we know that three plus four is
00:48	equal to seven . So in this equation X has
00:52	a value of three . But now let's talk about
00:59	a step by step process that will help us to
01:03	get this answer in this equation Access added to four
01:07	and that equal seven in order to solve the equation
01:10	. What you want to do is you want to
01:12	get the X variable by itself On one side of
01:15	the equation . The only way to do that is
01:18	to get rid of the four . So what you
01:21	need to do is perform the opposite operation of what
01:24	you see here . The opposite of addition is subtraction
01:29	. So we need to subtract both sides by four
01:34	. Whatever you do to the left side , you
01:35	must also due to the right side , Positive for
01:38	plus negative for it adds up to zero . So
01:40	they cancelled . Now we're gonna bring down the X
01:44	. And here we have 7 -4 , 7 -4
01:48	. Street . So we get X . Is equal
01:50	to three as we see here . So that's how
01:53	we could solve that particular linear equation . Now ,
01:58	for the sake of practice , go ahead and try
02:00	these two problems . X-plus nine is equal to 15
02:05	and also six plus X Is equal to 13 .
02:12	Feel free to pause the video and work on those
02:14	two examples . Now let's think about this intuitively what
02:19	number plus nine is equal to 15 ? We know
02:24	that six plus nine is 15 , So therefore X
02:28	. has to equal six . Now to show your
02:32	work . What you could do Is performed the opposite
02:35	operation of addition . So we c . Plus nine
02:39	. Let's attract both sides by nine . These two
02:43	will cancel we could bring down the X . And
02:46	so we'll get X . Is equal 2 15 -9
02:50	, 15 -9 is six . And for those of
02:55	you who may not be sure of that , what
02:57	you could do is you can use the number line
03:00	, Let's say if you have 15 here If you
03:03	want to subtract it by nine simply travel non units
03:06	to the left . So this is 14 13:12 11:10
03:17	9876 . So when you're subtracting , move to the
03:24	left using the number line . When you're adding just
03:27	move to the right . So that's how you can
03:30	do 15 -9 . Now let's work on the next
03:35	one . So here we have 6-plus sex is 13
03:40	. six plus . What number adds up to 13
03:43	? We know that 6-plus 7 Is 13 . So
03:47	therefore x . It's gonna be this # seven .
03:55	Now let's show our work what we need to do
03:57	in this example is the opposite of plus six .
04:01	We need to subtract both sides by six . So
04:06	these will cancel we can bring down the X .
04:10	And here we have 13 -6 which is seven .
04:13	So we get X . is equal to seven .
04:17	So that's how we could solve these one step linear
04:20	equation problems . What about these two problems ? X
04:27	-3 is equal to nine And N -8 is equal
04:34	to seven . Feel free to pause the video and
04:38	go ahead and calculate the value of X . And
04:41	the value of the variable end . So here we
04:46	see that X . is attracted by three to get
04:49	X by itself . We need to perform the opposite
04:52	operation of subtraction . The opposite of subtraction is addition
04:58	. So we need to add 3 to both sides
05:03	, -3 and positive fuel cancel . So we could
05:06	bring down the X . Variable . We'll get X
05:09	is equal to nine plus three . So the answer
05:13	is X is equal to 12 . And you can
05:17	check it . If you plug in 12 back to
05:19	the original expression , You'll get 12 -3 is equal
05:24	to nine And 12 -3 is nine . So the
05:27	left side is equal to the right side . That's
05:29	how you know if you have the right answer for
05:34	the next one , we could do the same thing
05:36	And this time we're going to add 8 to both
05:38	sides so we're going to have N . Is equal
05:44	to seven plus eight And 7-plus 8 is 15 .
05:49	So that's it for those two examples . Mhm .
05:55	Try these two . Let's say we have 6.3 is
05:58	equal to negative two plus Y . And then five
06:03	Is equal to a -8 . Go ahead and calculate
06:07	the value of why and the value of the variable
06:10	A . So this time why or the variable is
06:16	on the right side of the equation , not the
06:18	left side . So we want to get rid of
06:20	this negative too . So there's a negative sign in
06:23	front of the two . Therefore we need to perform
06:26	the opposite operation so we're going to add to to
06:29	both sides so that negative two and positive to will
06:34	cancel when you add them up , you get zero
06:36	. Mhm . Now let's bring down the y .
06:38	Variable . Here we have 6.3 plus two . So
06:44	to is the same as two point oh so if
06:50	you add them six plus two is eight 0.3 plus
06:55	point or just zero plus to history . So we
07:00	get why is equal to 8.3 For the next one
07:05	, We're going to add 8 to both sides ,
07:11	bringing down the A . We're gonna have a is
07:12	equal to five plus eight which is 13 . So
07:17	that's how we can solve those two linear equations .
07:21	Now I want to show you a technique that you
07:23	could use when solving linear equations . This technique might
07:29	be useful in some cases . So let's go back
07:32	to this equation . We're going to solve it two
07:34	ways . So the way that you're familiar with is
07:41	Adding seven . Since we have a negative seven here
07:44	, if we had seven to both sides and we
07:45	can quickly get the answer . So this is going
07:49	to be X . Is equal to 4-plus 7 which
07:53	is 11 . Another way in which you can get
07:56	that same answer Instead of adding seven to both sides
08:00	. What you can simply do is move the -7
08:03	from the left side to the right side . When
08:06	you move a number or variable from one side to
08:08	the other , the sign in front of it changes
08:12	. So we have a negative sign in front of
08:14	seven . One night when you move to seven to
08:17	the other side is going to be positive seven ,
08:20	it's a negative on the left but it's gonna be
08:22	positive on the right . So let's move this to
08:24	the other side . So what we're going to have
08:27	is X . is equal to four Not -7 but
08:31	plus seven . So it changed from negative 7 to
08:34	positive seven as you move it to the right side
08:38	And then 4-plus 7 11 . So that's another way
08:41	in which you can solve this equation . Let's try
08:46	that with this equation . Let's do it both ways
08:51	. So first we can subtract both sides by four
08:54	which is completely fine . If we do that we'll
08:58	get R is equal to 9 -4 which is five
09:05	. Or We could simply move the 4 to the
09:08	other side . It's positive for on the left but
09:12	it's going to be negative for the right And then
09:15	it's 9 -4 which will still give us the same
09:18	answer . Now go ahead and try these two problems
09:34	. So 5 -1 is equal to 12 . What
09:39	do you recommend that we should do to solve that
09:41	equation ? Would you add extra both sides ? subtract
09:49	both sides by five . What would you do for
09:54	this problem ? I recommend doing this . Let's take
09:57	a negative X . Move it and let's move to
10:00	the other side And then let's take positive 12 and
10:05	let's move it to this side . So let's focus
10:09	on the 12 , 12 is positive on the right
10:12	but it's going to be negative on the left ,
10:15	X is negative on the left side but it's going
10:18	to be positive on the right , positive X .
10:20	Is the same as just X . So now we
10:24	can see that X is simply 5 -12 . five
10:27	rounds 12 is -7 . So this is the answer
10:33	. I'm just gonna be right that answer here because
10:36	I'm going to show you the old fashioned way of
10:38	solving that equation . So here's what we could have
10:45	done to solve this problem . What we could do
10:50	is we can add X to both sides , but
10:56	I believe this is going to be the longer way
10:58	, So we'll get five is equal to 12 plus
11:01	ax . So we have positive X . Now instead
11:05	of negative X . And then we can subtract both
11:08	sides by 12 . So these will cancel on the
11:14	right side , we have X by itself on the
11:16	left , we have five minus 12 , Which is
11:18	-7 . So you could have done it that way
11:21	too . Both ways will work . Go ahead and
11:26	solve this one and let's use both techniques so feel
11:38	free to pause the video and try it . So
11:41	what I'm gonna do To get rid of some of
11:43	the negative signs is I'm going to move negative eight
11:47	to the right side and then I'm going to move
11:49	negative are to the left , so negative are as
11:54	I moved to the left is going to change the
11:55	positive are The five is going to remain where it
11:58	is the -8 , It's negative on the left side
12:02	. When I moved to the right side , it's
12:03	going to be positive eight . So whenever you move
12:06	a number or variable from one side to another ,
12:09	it simply flips sign it was negative , it becomes
12:11	positive . If it was positive it becomes negative .
12:14	So now I have R is equal to five plus
12:16	85 potatoes 13 . So that's one way in which
12:21	you could do it . The other way Is doing
12:23	it one step at a time . So first let's
12:26	add our to both sides . Negative R plus R
12:31	cancels Here we have negative eight plus are they're not
12:35	like terms , so we can't combine them . We
12:37	simply just have to rewrite them as negative eight plus
12:39	are Now we need to get our by itself so
12:44	we need to add 8 to both sides . And
12:49	these two will cancel , we could bring down the
12:52	R . And then we have five plus eight which
12:55	is 13 . So in both cases you can get
12:58	the same answer , you just have to pick which
13:00	method you prefer to work with . So that's how
13:03	we could solve that particular equation . Now let's say
13:08	we have three . X Is equal to 12 .
13:13	How can we calculate the value of X ? So
13:16	let's think about this intuitively three Times What Number is
13:21	equal to 12 ? When you see a number in
13:24	a variable attached like that . The connection between them
13:28	is most vocation . Three times what numbers ? 12
13:31	? We know that three times four is 12 .
13:34	Therefore X is equal to four in this example .
13:38	But now how do we show our work to get
13:40	this answer In order to get X by itself ?
13:44	We need to separate The X from the three in
13:48	order to separate it . We need to perform the
13:50	opposite operation of what we see here , The X
13:54	is multiplied by three . And what what operation is
13:59	opposite to multiplication ? We know that to be division
14:04	. So what we're gonna do is we're going to
14:05	use the division property of equality to get X by
14:08	itself . So we're going to divide both sides by
14:11	three . three . x divided by three Is one
14:17	. X . 3 divided by three is 1 .
14:18	So they cancel one . X is the same as
14:22	X . If you were to see a Z .
14:25	This is the same as one Z . If you
14:27	were to see why that's the same as one times
14:29	Y one times anything is itself . When you see
14:36	this fraction , It basically means Division 12 divided by
14:39	three . So while divided by three is 4 .
14:43	And so we get our answer . Acts is equal
14:44	to four . Go ahead and try this example Let's
14:50	say seven acts is equal to 14 . What is
14:53	the value of X ? So once again we're going
14:56	to use the division property of equality . We're going
14:59	to divide both sides by 7 to separate the seven
15:02	from the X . The 7s will cancel and we're
15:06	gonna get X . 14 divided by seven is too
15:10	that's the answer . X is equal to two .
15:17	Try these two , negative six . Y is equal
15:20	to negative 30 And -8 . N is equal to
15:25	48 . So go ahead and solve for the variables
15:28	why and end . So for this one all we
15:31	need to do is divide both sides by negative six
15:35	. So we can get why by itself -6 ,
15:38	divided by -6 is one . So we just get
15:41	why -30 divided by -6 . The two negative signs
15:46	will cancel . So that's the same as positive 30
15:49	divided by six and that's five 30 divided by six
15:56	is 5 and five times 6 is 30 . So
16:01	when you're thinking about What this answer is , if
16:03	you're asking yourself what is 30 divided by six ,
16:07	You can think of it this way , what is
16:08	six times what number is 30 ? And if you
16:11	know your multiplication tables , it's six times 56 times
16:14	five is 30 . So for the next one ,
16:18	what we need to do is divide both sides by
16:20	negative end , -8 divided by -8 is one .
16:25	So we just get in And here we divide in
16:28	48 by negative eight . Whenever you divide a positive
16:32	number by negative number , you're going to get a
16:34	negative result . So let's focus on 48 divided by
16:38	eight . What is 48 divided by 8 ? So
16:45	think of it in the other way , eight times
16:48	what number is 48 ? So using multiplication tables ,
16:54	hopefully you have that memorize . eight times 6 is
16:59	48 . Therefore 48 divided by eight is 6 .
17:03	So this is gonna be -6 positive 48 , divided
17:07	by -8 . His -6 . And you can confirm
17:10	that with your calculator . Try these two . Let's
17:16	say we have seven X . Is equal to negative
17:18	56 . A - eight Y . Is equal to
17:25	-72 . Go ahead and try those two problems .
17:31	So for the first one We need to divide both
17:34	sides by seven . The 7s will cancel on the
17:40	left given us X . And then what is -56
17:45	divided by positive seven . We know the answer is
17:50	gonna be negative . A negative number divided by a
17:52	positive number will give us a negative result . So
17:57	let's think of the let's think of it this way
17:59	. What is 56 divided by seven Or seven times
18:04	? What number is 56 ? Using your multiplication tables
18:10	you'll see that seven times eight is 56 . So
18:14	56 divided by seven is eight . Therefore -56 divided
18:18	by positive seven Must be -8 . Now moving on
18:25	to the next example , We need to use the
18:28	division property of equality . We need to divide both
18:31	sides by -8 . -8 will cancel on the left
18:36	. And so here we have . Why is equal
18:38	to negative 72 divided by -8 ? When you divide
18:42	two negative numbers , you're going to get a positive
18:44	result . So this is the same as dividing positive
18:47	72 by positive eight . Yeah . So what is
18:54	72 Divided by 8 ? What does that equal to
18:58	? Or eight times what number is 72 ? eight
19:03	times 9 is 72 ? Therefore 72 divided by eight
19:07	is 9 . So that's going to be the answer
19:10	for this example Why is equal to positive 9 ?

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This algebra video explains how to solve linear equations. It contains plenty of examples and practice problems.

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How To Solve Linear Equations In Algebra is a free educational video by The Organic Chemistry Tutor.

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