Good day students in this clip we are going to be going overan example on how to solve our
absolute value him so the instructions for this example
Is to solve
the given equation
and check your results okay and check your
result
alright so the problem under consideration is negative eight
minsus 2 times the absolute value
three minus two is equal to negative for forty
ok alright so how do we solve
absolute Value equation so lets
a real quick summary of the steps that we're going to execute
to find the value of n write down the steps
the steps are as follows so first your number one goal is to
to isolate the absolute value quantity
isolate the absolute value quantity
so if you look at this problem right here
this quantity right here is known as the absolute value quantity
so we want to get the aboslute value of 3n minus two isolated first
so that is the number one step. So secondly after doing that we are going to
to umm express as plus or minus
express as plus
or minus and switch it over
switch over the
plus or minus quantity because you know the absolute value of
of a quantity lets say the absolute value of x can be expressed as
as plus or minus x. So you express the absolute value as
a plus or minus quantity and you switch over
the plus or minus to the other side. And then the last step you will execute is to
seperate or split the equations and solve
and solve alright
Another thing to note when solving absolute
absolute value equations is that there are three possible solutions you can get
you can have two solutions one solution or no solution
Ok, but how is that possible? Well you can think of
The solution to an absolute value equation as an intersection between
an absolute value
function which is normally in the form of a v
and a line ok. Now if the line
intersects anywhere on
in the graph
If the absolute value quantity opens upwards like this
and the line intersects
intersects at the point that is higher than the vertex
like this how many solutions do you have? You have one solution here
and you have another solution here. So one possible solution you can have
Is two solutions
In this case you have two solutions
alright
like I said early there are three possible cases
So you can have two solutions. What of if the line intersects the absolute value functions
intersects the absolute value function
exactly at the vertex? If it intersects the vertex
here the vertex the iraqis you going to have exactly
one solution okay president and one
are X now the death I think we Sandusky
one solution I'm
now well in in ever increasing
the possibility right his keys you going to have
absolutely no solution I'm
so when your sole and absolute value the
it is very important read the lecture to deter me
our you to solutions I'm are
actually solutions working I was wishing on a solution
because you can still equating have solutions
it turns out there one of them is that a solution or
but that they learn in solution see a to be really careful insulin
absolutely be used to it check okay I still
arm let's go ahead and so that's a great thing
and in the process that so many times we want to keep he needs to
it's a review your out Google
we going to nap solutions are your okay
North keep that in mind now I'm her way so i three the absolute value
quantity base that is going to be right here in the absolute value
for their earning I throughly alright that'd be there are gay returning
8 birds in the area negate
few on with the other side right the result is
make it injury here I'm a good side in the play him
and then you have Nate's you
have the absolute value 3 and minus you
equal lani forty-fifth
aid native 30 right now
next going to do is it going to be the by Woodside lying naked thing
you I want to buy my ticket what happens is that by lightning
you you have any you there
and then he gonna happen absolute value re
n minus you equal to
by the DNC be know when he gets Yahoo 920 isolated acted
a good point check to see if you have any solutions not
value this is 40 in it can never have inning at the rally
so anything we have the afterburn on the isolated
a good number to the right doing it for you at a graphically
does he have no solution you get happy keys right here
alright to get a good grade teacher who have doubts about being in court
you it by the number so it can't be that don't have at least one solution
alright we don't step one which is to isolate the absolute value
already know it when this happens there again expresses absolute value as
also minus 3 a.m. minus you
equal 16
now not to pursue my tits over we going in the Bible sites right person -1
the lower was a minus-1 arrangement -1
or even just for the bottom line is over it's not firms so they have
3 and lines you people
Western -16 alright
now have that want to execute that not to laugh that is
maybe region all how do we do that
at least week equally here well
we have but the line is here to it wants to dance with
the happen right again is that it into the laity
component three and nine hits you people living in 16
in the positive Polly realign its you pools but it's the
alright the landfill the first one so this with the
at you in the directory as they didn't do that
the goods I we have 3n
equal -14 in the ballots I
3 583 every 3
any our an the rolls negative
14 over very now and it's a great here either
at here I here
it really for me
and I would sign barry 3
Indiana in equal
six all right sir solutions that her
me working and six so we have to do it can't get to make your
anger okay even though we were wiped out earlier on Sat they don't forget to
I was there the fact that the creators all the hits keep going
blindly but he doing credit has the catcher or
so dedicated breast cancer which is enable the
14 over three but I see the stars by the original intriguing
being for the questionnaires on is legally
a minus you time isolated probably
your writing times 3
now than a plugin best solution we have originated 14
3 at on
my next you equally
for him that the question right as the incident
by these Hadley a line is you dreaded be cancelled out that we have absolute
value only
fourteen miners you is that people
the forty as well for doing it
in minus you minus 20 minutes -16
that both the forty
now they have native a minus you absolute value
think think it's 6816 it really
or feeling for you me they have nearly
me -30 you reporting
already in the final question is -40
equal to 1840 yesterday years
confident that our first solution in fact
her or check the second one
on kick and
in polls sick so the question here is
is negative a minus few
times 3 kinds rug in the answering that which is 6
returns 6
mine you in the people
today forty at birth right it's working out plea
a improprieties with a handgun
naming you times the taxes exist 18
be I'll
mine is you absolute value
the putting in forty in any
a running you eighty minutes least think the apt about it 16
it equally 40 after the onion
think its eggs in a hurry care who hears that he would change his native sixteens
ass about it but its sixteen
16 the team 10 16
reporting important your order operations market by
earth mainly a -30 you equally important
may in my tits on -30
using 14 need forty
Courtney forty the answer is yes so that works out
also okay confident that our solution
are going to be in is people in
being important you know what they re
Aaron 106 alright still
back there thanks so much for taking the time to wear this presentation could be
suspect like a link between here are the style huard
it such as this he's good for you with the comment
let me know what you think about this clip
more math videos can be found on mathgotserved.com/algebra2
outwards that
so thank you for watching that have a wonderful day