Algebra Shortcuts - Work smarter and faster! - Free Educational videos for Students in K-12

Algebra Shortcuts - Work smarter and faster! - By tecmath

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00:0-1	get a welcome to Tech mouth channel . I'm josh
00:02	in this video . We're going to be looking at
00:03	the three best algebra shortcuts for saving you a stack
00:07	of time in algebra And these are absolute crackers by
00:10	the way . You will not see these in school
00:12	. So I recommend you a bit of a look
00:13	because they will save you a ton of time .
00:15	So let's just launch straight into a Okay for the
00:19	first trick . So we had an algebraic equation as
00:21	follows . We had three X . And that's plus
00:25	five . All that divided by four is equal to
00:29	eight . And what we want to do is we
00:30	want to solve X pretty much instantly as fast as
00:33	we can . Now the way that we do this
00:35	is as follows . Obviously you won't have to write
00:38	this down . I'm just going to be writing it
00:40	down to show you . So owner have a look
00:43	what's happening to Xia . So X Is first off
00:46	being multiplied by three . They were adding fire to
00:50	it . Then we're dividing the whole lot by four
00:53	and that is equal to eight . Now the way
00:56	we're going to solve this is we are going to
00:58	work backwards . Uh we're going to start at the
01:00	age here we're gonna work the way backwards but what
01:03	we're gonna do is we're going to the opposite operation
01:05	as to what is happening , we're not gonna worry
01:07	about bob maceio . So where it's dividing by four
01:11	, we're going to multiply by four Where it's adding
01:14	five , we're going to subtract five where it's multiplied
01:17	by three . We are going to divide by three
01:20	and this will give us the answer for X .
01:23	So let's do this , we're going to start at
01:24	eight and we are going to head backwards so eight
01:28	multiplied by four . He's 32 minus five Is 27
01:35	and then divided by three . Well 27 divided by
01:38	three X is equal to nine . Now look you
01:42	can actually do this straight away , you can literally
01:43	just go eight multiplied by four minus five , Divide
01:48	by three and you'd have your answer . So it's
01:50	a really , really handy trick for doing algebra equations
01:54	like this straight away . What about we do one
01:56	more ? Okay , what about one more of these
01:58	? We have the following example , we have four
02:01	X . And to this we're adding three . The
02:05	whole lot of that's sitting in brackets and it's being
02:07	multiplied by two and this is equal 2 46 .
02:12	And what we're trying to work out is we are
02:14	trying to work out what X . Is equal to
02:16	. Now looking at this , be honest , if
02:18	I was doing this I would start at the 46
02:21	here and I'll just move straight into it without writing
02:23	all this down . I'm beginning 46 Divided by 2
02:27	-3 , find about four and I will have my
02:30	answer there . But I'm going to show you each
02:32	step on how I'm doing this because I'm sort of
02:35	seeing a few things as we do this . So
02:37	what we're doing is we are starting with Xia and
02:41	the first thing we're doing is it's multiplied by four
02:44	, it's then adding three to it . It's then
02:47	multiplied by two And this is equal to 46 .
02:51	So what we're going to be doing and that's what
02:53	I started out here literally just started doing the opposite
02:56	. We're going to be divided by two , we're
02:59	going to be subtracting three and then we're going to
03:01	divide by four and that will give us our answer
03:05	. So let's go through and do that . 46
03:08	Divided by two . The answer is 23 -3 ,
03:12	that is 20 and divided by four x Is equal
03:17	to five . Now look , you could do that
03:19	straight away with just going off this . 46 divided
03:22	by two is 23 Born us three . He's 20
03:26	Divided by four . We get our answer of five
03:29	. So that's the first shortcut trick for working out
03:32	some algebra equations . Really , really simple . Really
03:34	, really fast . Let's get on the trick number
03:37	. So okay , the trick number two . And
03:40	this works with these following types of expressions where we
03:43	have something like four X plus one and this is
03:47	equal to three X Plus four and what we want
03:51	to do is we want to solve what X equals
03:54	. Now the way we can do this is really
03:56	, really quick . We don't have to actually rewrite
03:58	things out a whole bunch of times where you're going
04:00	to just work this out straight underneath here . We
04:03	want to get all the experts on one side and
04:05	all the numbers on the other side and we're just
04:08	going to solve for what X is then . So
04:10	we have a look at our exes first , you
04:12	can see we have four X . And we have
04:14	three X . So I'm going to get rid of
04:16	the threats off this side by subtracting it . It's
04:18	just going to get rid of it . And I'm
04:20	also going to do the same on this side ,
04:22	so minus three X . I'm also going to want
04:26	to get rid of the one on this side and
04:28	get it over here . So take away one .
04:31	I'm going to get rid of that here and I'm
04:32	going to take that one of that side there and
04:34	now I can work this out directly . So let's
04:36	go through and do this four X . Take away
04:40	three X . This is equal to X . Four
04:43	Take away one . This is equal to three .
04:46	We have our answer that X . Is equal to
04:49	three . Now let's just sub in just to make
04:51	sure that our answer is good . It's always a
04:53	good policy to do that when you're first working things
04:55	out . So it wouldn't do that . If X
04:58	is equal to 34 Times three is equal to 12
05:01	, 12 plus one is equal to 13 and three
05:07	times three is equal to 99 plus four is also
05:10	equal to 13 . And we've got the right answer
05:13	there . So what about we do one more example
05:15	of these ? Okay let's do one more example of
05:18	these . We have five X plus two and that
05:24	is equal to three X minus six . Okay we're
05:29	trying to work out what X equals . Once again
05:31	really simple . So we're going to get all the
05:33	exes on one side . So let's get rid of
05:35	this three xia . Take it away . We're going
05:38	to do the same over here so take away three
05:40	X . We're gonna get rid of that to their
05:42	by taking it away . We're going to take it
05:44	away also on this side . So now let's work
05:47	out what we have five x minus three X .
05:49	This is equal to two X and minus six minus
05:53	two . This is equal to minus 82 X is
05:57	equal to minus eight . Therefore X is half of
06:00	that which is equal to minus four X . I
06:03	think it was -4 . Should we check that out
06:06	? Why not ? Okay so here we were to
06:07	do that this is what we're going to get .
06:10	Five times minus four is minus 20 Plus two is
06:15	-18 . three times -4 is negative . 12 -6
06:21	is also -18 and therefore our answer is correct .
06:25	So it's the second trick for algebra , it saves
06:28	a whole stack of time . Right . What about
06:30	I show you one more . Okay . To our
06:32	third algebra shortcut , what we're going to be having
06:35	a look at is simultaneous equations . So I'll just
06:37	put a set of simultaneous equations up and then I'll
06:40	show you how to work this out directly . So
06:43	let's go through and do that . We have the
06:44	following , we have three X plus , Y is
06:48	equal to 10 and then two X plus . So
06:52	why Is equal to 12 ? Just a couple of
06:56	things here , you are going to have to remember
06:58	a little pattern that you used to work this out
07:01	. It just is the other thing is is where
07:03	you have a wire like this here , there is
07:06	a one there . We don't bother draw it in
07:08	, but there is a one there and we are
07:09	going to be using the coefficients the numbers in front
07:11	of these variables . So we need to know that
07:13	. So the following pattern is going to be used
07:16	. We're gonna work at X first . So first
07:18	off , what we're going to do is we're going
07:20	to multiply , we're gonna start at the top here
07:21	, this number by this number , And then there's
07:24	no more by this number . So the why and
07:25	the answer and the why and the answer . So
07:28	one times 12 Is equal to 12 and two times
07:32	10 , which is 20 . And we're subtracting there
07:36	. Okay , this all goes over and now what
07:39	we're gonna do is we are going to have the
07:41	one times two here , one times two . And
07:45	the three times too . So let's do this one
07:48	, times two is equal to two , and three
07:51	times two is equal to six . Also going to
07:53	be subtracting here . So what happens when we do
07:55	this ? We have the following 12 . Take away
07:58	20 is equal to negative eight . This goes over
08:02	the top of two . Well the six which is
08:04	-4 . And we have our answer negative eight divided
08:07	by negative for our answer is two , X is
08:11	equal to two . And then we work out why
08:14	as well , we go through a similar process but
08:16	I reckon it's fastest to sub in . So let's
08:18	do that . What do we have ? We have
08:20	uh X is equal to two , so three times
08:22	two is equal to 66 plus Y . Is equal
08:26	to 10 . 6 plus what is equal to 10
08:28	? Well that would be for that's our answer .
08:31	Let's just check to see that worked . Okay ,
08:32	so uh two times two is equal to four Y
08:35	. Is four , so two times four is 84
08:39	plus eight is equal to 12 or grew . So
08:43	just remember that pattern and you will be fine and
08:45	it works each time . So what about to put
08:47	another one of these up ? Okay . Let's have
08:50	a look at another . One of these will make
08:51	it a bit harder this time we have the following
08:54	, we have three x Plus two . Y .
08:59	is equal 27 And then we have five x -3
09:05	Y . Which is equal to 37 . Now ,
09:09	just a couple of notes of caution here , we
09:11	have this negative here . Just watch out for that
09:13	. It's going to be the undoing of you if
09:15	you're not careful and you'll get all sorts of funny
09:17	answers if you don't pay good attention . So you
09:21	know , we'll just make sure we paid attention as
09:23	we're going along . So first off we're going to
09:25	work out what X . Is equal to once again
09:28	we're going to be doing that same pattern two times
09:31	37 7 Times -3 . Just make sure we're using
09:36	that negative three there . Okay , so let's go
09:38	through and do that to multiply by 37 . Well
09:42	that's going to be 74 . We have seven Times
09:48	-3 which is equal to -21 . We're going to
09:51	be taking that away so it's going to turn that
09:53	into a plus 21 . Okay cool . Just watch
09:57	out for that . Like I said okay so now
10:00	let's go through a workout the next bit , we
10:02	have two times five which is equal to 10 and
10:06	we also have three Time to -3 which is equal
10:10	to -9 . We're gonna be taking that away ,
10:12	so it's going to make that into a positive also
10:14	. So plus nine . Now when we work this
10:17	out , what do we get ? We have 74
10:20	plus 21 which is equal to 95 10 plus nine
10:26	, which is equal to 1995 divided by 19 .
10:31	We have our answer X . Is equal to five
10:34	. So let's just write that in right there .
10:36	X is equal to five . Now we go through
10:40	and we just sub so let's just do that three
10:43	times five is equal to 15 , 15 plus two
10:47	, Y is equal to seven . So how are
10:49	we going to get to seven ? So if 15
10:52	plus two , Y is equal to seven . We
10:55	could use that other trick that we did before where
10:58	what we're going to be doing is we know that
11:00	the first thing that's happening is why is market buying
11:02	by two adding 15 ? And that is the seven
11:07	. Let's just do the opposite . So seven Take
11:11	away 15 . That's going to be negative eight divided
11:15	by two is equal to negative for Y is equal
11:19	to negative for Okay , so there you go .
11:22	You have three tiny little algebra shortcut tricks that even
11:26	as you can see they integrate with one another and
11:28	they work just to treat . So hopefully you do
11:31	like these and if you like this video give me
11:32	a thumbs up and tell me what you think .
11:34	Now if you have any other algebra shortcuts , I'll
11:36	talk to the ones where we're talking a perfect square
11:39	and what sort of deal I'm talking ones you generally
11:41	won't get taught by your math teacher . Put in
11:43	the comments below . I'd really love to hear about
11:46	them . Anyway , we'll see you next time boy
00:0-1	.

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