Algebra Basics: Solving 2-Step Equations - Math Antics - Free Educational videos for Students in K-12

Algebra Basics: Solving 2-Step Equations - Math Antics - By Mathantics

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00:03	Uh huh . Hi , I'm rob . Welcome to
00:07	Math antics . In the last two algebra videos ,
00:10	we learned how to solve simple equations that had only
00:13	one arithmetic operation in them . But often equations have
00:16	many different operations , which makes solving them a little
00:19	more complicated . In this video we're going to learn
00:22	how to solve equations that have just two math operations
00:25	in them . One addition or subtraction and one multiplication
00:29	or division . And the concepts you learn in this
00:31	video will help you solve even more complicated equations in
00:35	the future . Now as you might expect equations that
00:38	have to arithmetic operations in them are going to require
00:41	two different steps to solve them . In other words
00:45	, to get the unknown all by itself , you'll
00:46	need to undo two operations but that doesn't sound too
00:50	hard right ? I mean we learn how to undo
00:52	any arithmetic operation in the last two videos and that's
00:56	true but there's a couple reasons that make two step
00:58	equations a little trickier to solve . The first is
01:02	that there's a lot more possible combinations of those two
01:05	operations . And the second is that when there's more
01:08	than one operation you have to decide what order to
01:11	undo those operations in . Hello , If you need
01:15	to know what order to do operations in , just
01:18	follow the order of operations Rules , you did watch
01:20	that video , didn't you ? I sure did .
01:24	But the order of operations rules tells us what order
01:27	to do operations , not what order to undo them
01:30	. Oh well then could we reverse the order ?
01:35	Since we're undoing the operations ? Now that's a good
01:38	idea ? Well of course it is . When solving
01:41	multi step equations , that's basically what we're going to
01:44	do . Using the order of operations rules in reverse
01:48	can help us know what order to undo operations in
01:51	but it can be a little tricky actually putting it
01:54	into practice so to see how it works . Let's
01:57	start by solving a very simple two step equation .
02:00	two x plus two equals 8 . In this equation
02:04	, the unknown value X . Is involved in two
02:07	different operations , addition and multiplication which is implied between
02:12	the first two and the X . And to undo
02:15	those two operations we need to use their inverse operations
02:18	, subtraction and division . But the question is ,
02:21	which one should we do first ? Like many things
02:24	in life . The order we decided to do things
02:26	in can make a big difference . No . Oh
02:30	come on . There's gotta be an easier way .
02:33	First sucks 10 shoes . Fortunately in math we have
02:38	a special set of rules that tell us what order
02:40	to do operations in those rules tell us to do
02:44	operations inside parentheses or other groups first and then we
02:48	do exponents and then we do multiplication and division and
02:52	last of all we do addition and subtraction . Those
02:55	are the rules you need to follow when simplifying mathematical
02:58	expressions or equations . But solving an equation is different
03:02	because we're trying to undo any operations that the unknown
03:05	value is involved with so that the unknown value will
03:08	be all by itself . So when solving equations the
03:11	best strategy is to apply those order of operations rules
03:15	and reverse . Using the reverse order of operations is
03:18	not the only way to solve a multi step equation
03:21	but it's usually the easiest way just like it's much
03:24	easier to take your shoes and socks off in the
03:27	reverse order that you put them on . Yeah .
03:31	Are you sure ? It sucks before shoes . Since
03:35	the order of operations rules tell us to do multiplication
03:39	. Before we do addition . We should undo addition
03:43	before we undo multiplication . So first we undo the
03:48	addition . By subtracting two from both sides of the
03:51	equation . On the first side the plus two and
03:55	the minus two cancel each other out , leaving just
03:58	two X . On that side . And on the
04:00	other side we have 8 -2 which is six .
04:04	Next we can undo the multiplication by dividing both sides
04:09	of the equation by two . On the first side
04:12	the two's cancel leaving X all by itself . And
04:16	on the other side we have six divided by two
04:19	which is just three . There . We saw the
04:22	equation using the order of operations rules in reverse and
04:26	now we know that X equals three . That wasn't
04:29	so bad was it ? Let's try solving another simple
04:32	two step equation that has division and subtraction in it
04:36	. X over two minus one equals four . Again
04:40	we're going to apply the order of operations rules in
04:43	reverse to undo the subtraction and the division operations .
04:47	Since we would normally do the subtraction last , we're
04:50	going to undo it first to undo the subtraction .
04:54	We add one to both sides of the equation .
04:56	On the first side the minus one and the plus
04:59	one cancel out leaving just X over two on that
05:02	side . And on the other side we have four
05:05	plus one which is five . And then to undo
05:09	the divided by two , we need to multiply both
05:12	sides by two . On the first side the two's
05:15	cancel leaving X all by itself . And on the
05:18	other side we have two times 5 which is 10
05:21	. So our answer is x equals 10 . Those
05:24	examples are pretty easy . Right ? But solving to
05:27	step equations gets a bit trickier . Thanks to a
05:30	little something in math called groups . Do you remember
05:33	how parentheses are used to group things in math ?
05:36	And our order of operations Rules say that we're supposed
05:39	to do any operations that are inside parentheses first .
05:42	In other words we need to do operations that are
05:45	inside of groups first . Well guess what that means
05:49	that when we're solving equations and undoing operations we need
05:52	to wait to do groups last of all to see
05:56	what I mean . Let's solve this equation which looks
05:58	very similar to the first one we solved . The
06:01	only difference is that a set of parentheses has been
06:04	used to group this X-plus two together . And even
06:07	though that might not seem like much of a change
06:09	makes a big difference for our answer . That's because
06:12	in the original equation , this first two is only
06:16	being multiplied by the X . But in the new
06:18	equation it's being multiplied by the entire quantity or group
06:23	X-plus two . And that's going to change how we
06:25	solve it . We're still going to follow our order
06:28	of operations rules in reverse . But now that the
06:31	X plus two is inside parentheses , which means that
06:34	it's part of a group . We're going to undo
06:36	that operation last since we're supposed to do operations and
06:40	groups first , it means that we're going to undo
06:43	operations and groups last . So in this problem we
06:46	should start by undoing the multiplication that's implied between the
06:50	two and the group X-plus two . To do that
06:54	, we divide both sides of the equation by two
06:58	on the first side , the two on the top
07:00	and the two on the bottom cancel , leaving the
07:03	group X plus two on that side . And on
07:06	the other side We have eight divided by two which
07:09	is four . That looks simpler already . And we
07:12	can make it even simpler than that because now that
07:15	there's nothing else on that side of the equal sign
07:17	with the group X plus two , we really don't
07:20	even need the parentheses anymore . Next we just need
07:24	to subtract two from both sides . On the first
07:26	side , the plus two and the minus to cancel
07:29	out Leaving X all by itself . And on the
07:32	other side we have 4 -2 which is two .
07:36	So for this equation x equals two . And now
07:39	you can see how grouping operations differently in our equation
07:43	results in different answers . Let's try one More important
07:47	example , do you remember the second equation we solved
07:50	X over two minus one equals four In this equation
07:54	the one is being subtracted from the entire X over
07:58	two term . But take a look at this slightly
08:01	different equation . This looks a lot like the original
08:03	equation but now that the one is up on top
08:06	of the fraction line , it's only being subtracted from
08:08	the X and not the two . The X -1
08:11	on top forms a group . Hold on . How
08:14	can X -1 be a group ? I don't see
08:16	any parentheses or brackets around him . Ah That's a
08:20	good question . In algebra . The fraction line is
08:23	used as a way to automatically group things that are
08:26	above it or things that are below it . For
08:28	example , in this fancy algebraic expression , everything that's
08:32	on top of the fraction line forms a group and
08:35	everything on the bottom of the line forms another group
08:38	. Of course we could put parentheses there if we
08:40	wanted to make it really clear , but it's not
08:43	required grouping above and below . A fraction line is
08:47	just implied in algebra . Getting back to our new
08:50	problem , now that we know that the X -1
08:53	on the top of the fraction line is an implied
08:55	group . As we learned in our last example ,
08:58	we're going to wait and undo the operation inside that
09:01	group last . So the first step is to undo
09:05	the divided by two by multiplying both sides of the
09:08	equation by two . On the first side , the
09:11	two on the top and the two on the bottom
09:13	will cancel out . Leaving just are implied group X
09:16	-1 on that side . And on the other side
09:20	we have four times two , which is eight .
09:23	Next we can undo the operation inside the group by
09:26	adding one to both sides . On the first side
09:29	, the -1 and the plus one , cancel leaving
09:32	X all by itself . And on the other side
09:35	we have eight plus one which is nine . So
09:38	in this equation x equals nine . All right .
09:42	As you can see , solving to step equations is
09:45	definitely more complicated than single step equations because there's so
09:50	many different combinations and different ways to group things .
09:53	But if you just take things one step at a
09:55	time and remember to undo operations using the reverse border
10:00	of operation rules , it will be much easier .
10:03	Just pay close attention to how things are grouped in
10:05	an equation and be on the lookout for those implied
10:08	groups on the top and bottom of a fraction line
10:11	. And because there's so many variations of these two
10:15	step equations , it's really important to practice by trying
10:18	to solve lots of different problems , as always .
10:21	Thanks for watching Math Antics and I'll see you next
10:23	time learn more at Math Antics dot com .

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