Algebra Basics: Solving Basic Equations Part 1 - Math Antics - Free Educational videos for Students in K-12

Algebra Basics: Solving Basic Equations Part 1 - Math Antics - By Mathantics

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00:03	Uh huh . Hi , I'm rob . Welcome to
00:07	Math antics . In our last algebra video , we
00:10	learned that algebra involves equations that have variables or unknown
00:14	values in them . And we learned that solving an
00:17	equation means figuring out what those unknown values are .
00:21	In this video , we're going to learn how to
00:23	solve some very simple algebraic equations that just involve addition
00:27	and subtraction . Then in the next video we'll learn
00:30	how to solve some simple equations involving multiplication and division
00:33	. Are you ready ? I thought so . Okay
00:37	. So if you've got an equation that has an
00:39	unknown value in it , then the key strategy for
00:42	solving it is to rearrange the equation until you have
00:45	the unknown value all by itself , on one side
00:48	of the equal sign and all of the known numbers
00:51	on the other side of the equal sign . And
00:53	then you'll know just what the unknown value is .
00:56	But how do we do that ? How do we
00:58	rearrange equations ? Well , we know that algebra still
01:02	uses the four main arithmetic operations , addition , subtraction
01:06	, multiplication and division . And we can use those
01:09	operations to rearrange equations as long as we understand one
01:14	really important thing . First we need to understand that
01:17	an equation is like a balance scale . You've seen
01:20	a balance scale right ? If there's the same amount
01:23	of weight on each side of the scale then the
01:26	two sides are imbalanced , but if we add some
01:30	weight to just one side then the scale will tip
01:35	. The two sides are no longer imbalance . An
01:38	equation is like that whatever is on one side of
01:41	the equal sign must have exactly the same value as
01:45	whatever is on the other side . Otherwise the equation
01:49	would not be true . Of course that doesn't mean
01:51	that the two sides have to look the same .
01:54	For example in the equation one plus one equals 21
01:58	plus one doesn't look like the number two , but
02:01	we know that one plus one has the same value
02:04	as to so one plus one equals two is in
02:07	balance . It's a true equation . The reason we
02:10	need to know that equations must be balanced is because
02:13	when we start rearranging them , if we're not careful
02:16	we might do something that would change one side more
02:19	than the other . That would make the equation get
02:22	out of balance and it wouldn't be true anymore .
02:24	And if that happens , we won't get the right
02:26	answer when we solve it . That sounds pretty bad
02:29	. Huh ? So how do we avoid that ?
02:32	How do we avoid getting an equation out of balance
02:35	? The key is that whenever we make a change
02:38	to an equation , we have to make the exact
02:40	same change on both sides . That's so important .
02:44	I'll say it again . Whenever we do something to
02:47	an equation , we have to do the same thing
02:50	to both sides . For example , if we want
02:53	to add something to one side of an equation ,
02:55	we have to add that same thing to the other
02:58	side . And if we want to subtract something from
03:01	one side of an equation , then we have to
03:03	subtract that same thing from the other side . And
03:07	that's the same for multiplication and division . If we
03:10	want to multiply one side of an equation by a
03:12	number , then we need to multiply the other side
03:15	by that same number . Or if we want to
03:17	divide one side of an equation by a number ,
03:19	then we have to divide the other side by that
03:21	number . Also , as long as you always do
03:25	the same thing to both sides of an equation ,
03:27	it will stay in balance and your equation will still
03:30	be true . All right . Like I said in
03:34	this video , we're just going to focus on equations
03:36	involving addition and subtraction . And here's our first example
03:41	, X-plus seven equals 15 to solve for the unknown
03:46	value X . We need to rearrange the equation so
03:49	that the X is all by itself on one side
03:52	of the equal sign . But what can we do
03:54	to get X all by itself ? Well , right
03:57	now , X is not by itself because seven is
04:00	being added to it . Is there a way for
04:02	us to get rid of that ? 7 ? Yes
04:05	. Since seven is being added to the X .
04:07	We can undo that by subtracting seven from that side
04:10	of the equation , subtracting seven would leave X all
04:14	by itself because X plus seven minus seven is just
04:19	X . The Plus seven and the -7 cancel each
04:22	other out . Okay , great . So we just
04:26	subtract seven from this side of the equation and excess
04:28	all by itself equation solved right wrong . If we
04:33	just subtract seven from one side of the equation and
04:36	not the other side then our equation won't be in
04:39	balance anymore to keep our equation and balance . We
04:42	also need to subtract seven from the other side of
04:45	the equation . But on that side we just have
04:48	the number 15 . So we need to subtract seven
04:51	from that 15 . And since 15 -7 equals eight
04:56	, that side of the equation will just become eight
04:59	there by subtracting seven from both sides . We've changed
05:02	the original equation , X plus seven equals 15 into
05:06	the new and much simpler equation X equals eight ,
05:10	which tells us that the unknown number is eight and
05:13	we've solved the equation And to check our answer to
05:17	make sure we got it right , we can see
05:19	what would happen . If we replace the unknown value
05:22	in our original equation with the number eight instead of
05:26	X plus seven equals 15 , we would write eight
05:29	plus seven equals 15 . And if that's true then
05:32	we know we got the right answer . Pretty cool
05:35	. Huh ? Let's try another 1 . 40 equals
05:38	25 plus X . This time the unknown values on
05:42	the right hand side of the equation . Does that
05:44	make it harder ? Nope . We use the exact
05:46	same strategy . We want to get X by itself
05:50	. But this time X is being added to 25
05:53	. But thanks to the community of property , that's
05:55	the same as 25 being added to X . So
05:58	to isolate X , we should subtract 25 from that
06:02	side of the equation . But then we also need
06:04	to subtract 25 from the other side to keep things
06:07	in balance On the right side , X-plus 25 -25
06:13	is just X . The -25 cancels out the positive
06:17	25 that was there . And on the other side
06:20	we have 40 -25 which would leave 15 . So
06:25	the equation has become 15 equals X , which is
06:29	the same as x equals 15 . Again we've solved
06:33	the equation . So whenever something is being added to
06:36	an unknown , we can undo that and get the
06:39	unknown all by itself by subtracting that same something from
06:43	both sides of the equation . But what about when
06:46	something is being subtracted from an unknown , like in
06:49	this example X -5 equals 16 . In this case
06:55	X is not by itself because five is being subtracted
06:58	or taken away from it . Any ideas about how
07:01	we could get rid of or undo that -5 ,
07:04	yep . To undo that subtraction this time , we
07:08	need to add five . The both sides of the
07:10	equation , The -5 and the Plus five cancel each
07:14	other out and leave X all by itself on this
07:17	side . And on the other side we have 16-plus
07:21	5 which is 21 . So in this equation x
07:25	equals 21 . Let's try another example like that ,
07:29	10 equals X -32 . Again the X is not
07:34	by itself because 32 is being subtracted from it .
07:38	So to cancel that -32 out , we can just
07:41	add 32 to both sides of the equation . On
07:45	the right side , the minus 32 the plus 30
07:48	to cancel out . Leaving just X . And on
07:52	the left side we have 10 plus 32 which is
07:56	42 . Now we know that X equals 42 .
08:01	Okay , so now you know how to solve very
08:04	simple equations like these , where something is being added
08:07	to an unknown or something is being subtracted from an
08:10	unknown . But before you try practicing on your own
08:13	, I want to show you a tricky variation of
08:15	the subtraction problem that confuses a lot of students .
08:19	Do you remember how subtraction does not have the community
08:22	of property ? If you switch the order of a
08:25	subtraction , it's a different problem . Suppose we get
08:28	a problem where instead of a number being taken away
08:31	from an unknown , an unknown is being taken away
08:34	from a number . What do we do in that
08:36	case ? Well , we still want to get the
08:39	unknown all by itself , but it's a little harder
08:42	to see how to do that In this problem .
08:44	12 -X equals five . The 12 on this side
08:48	is a positive 12 . So we could subtract 12
08:51	from both sides . That would get rid of the
08:53	12 . But the problem is that want to get
08:56	rid of the minus sign , that's because the minus
08:59	sign really belongs to the X . Since it's the
09:02	exits being subtracted , subtracting 12 would leave us with
09:06	negative X . On this side of the equal sign
09:08	, which is not wrong , but it might be
09:10	confusing if you don't know how to work with negative
09:13	numbers . Yet , fortunately there's another way to do
09:16	this kind of problem that will avoid getting a negative
09:19	unknown Instead of subtracting 12 from both sides . What
09:23	would happen if we added X to both sides ?
09:26	Can we do that ? Can we add an unknown
09:28	to both sides ? Well , sure why not ?
09:32	We can add or subtract anything we want as long
09:35	as we do it to both sides and when we
09:38	do that the minus X and the plus X will
09:41	cancel each other out on this side . And on
09:43	the other side we get five plus X . Now
09:47	our equation is 12 equals five plus X . And
09:51	you might be thinking but why would we do that
09:54	? That didn't even solve our equation . Ah That's
09:57	true but it changed it into an equation that we
10:00	already know how to solve now . It's easy to
10:03	see that we can isolate the unknown just by subtracting
10:07	five from both sides of the equation and that will
10:10	give us seven equals X . Or x equal seven
10:13	. It just took us one extra step to rearrange
10:16	the equation but then it was easy to solve .
10:19	Okay that's the basics of solving simple algebraic equations that
10:24	involve addition and subtraction . You just need to get
10:27	the unknown value all by itself and you can do
10:30	that by adding or subtracting something from both sides of
10:34	the equation . And this process works the same even
10:38	if the numbers in the equation are decimals or fractions
10:41	and it also works the same . No matter what
10:43	symbol you're using for an unknown , it could be
10:46	X , y , z or abc . The letter
10:49	being used . Doesn't matter remember when it comes to
10:52	math . It's really important to practice what you've learned
10:56	. So be sure to try solving some basic equations
10:58	on your own . As always . Thanks for watching
11:01	mathematics and I'll see you next time learn more at
11:05	math Antics dot com .

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