Hello, Assalamualaikum.
Hi everyone.
So today we are in part 3 of
inequalities
at the end of this video.
You should be able to solve
quadratic inequalities by
using either graphical or
analytical method.
But in this video, I only use
analytical method
Which called table of sign
alright guys, this is
A picture of the world of
science.
Okay, just a sample of people
of sign.
I'm going to explain to you
briefly before we go deeper
in the example later.
Okay, first you are going to
get a question like this.
Okay
any quadratic equation, so you
need to rearrange and
factorize it?
Okay.
So the final product
factorization must be looking
like this.
Okay.
The left hand side is the
factorised product or the
factor a quadratic
and the right hand side must be
zero.
Okay, so no matter what
direction.
Okay, so negative 1 and 2 you
will get from the factorization.
Okay, I'm sure you all know how
to get this value.
Okay, just let it go deeper and
you get this value.
Yeah.
So now
in the table the first column
you need to list down all the
factorised.
Okay.
So we have x + 1
because
this factor this 2 Factor
multiplied each other.
So in the final product here we
need to multiply it.
As well.
Okay.
So next
in the first row row means this
Row the in the first row we
need to
list.
We need to write down the
interval.
Okay.
So interval came from interval
is from negative Infinity
until positive Infinity.
So you need to arrange it in
ascending order.
Okay.
So because negative 1 come
first before 2
and we know that infinity
always open bracket
what about -1 and 2. So back
to this green box.
The inequality doesn't have
equal sign, hence.
It is an open bracket and then
there's value
For test value
You can put any number in
between the respected intervals.
Okay.
I have -2 within this
interval.
Also.
I have zero with the negative 1
& 2
also, I have three within
to until Infinity you can put
99 if you want you can put 86
if you want.
Okay, but always choose the
easier number to calculate
because we want to put -2, 0 and 3 in x here.
So if I put them in x+1 I will get
okay.
Let's say 0 I put it in x + 1, 0+1 is 1 it's a positive
number.
Hence.
That's why I put a positive
here.
Okay.
So, let's see for x - 2
Then we're
going to multiply these two and
get the final sign.
Okay.
Now the final answer which
interval will be our answer.
Okay, look back again in our
green box here
because it wants less than 0 it
means the answer or the
interval must have a negative.
Okay.
So which interval has negative
sign
is it this one?
No, is it this one?
Yes.
This interval has a
negative sign
hence our answer if we're going
to write it in interval form.
It is just (-1,2)
You just you can just copy it
again so easy and if the
question asks you to write
inside form,
okay, just write down the usual
bracket because X is between
negative 1 & 2 x should be In
the middle,
the direction of the inequality
is always towards left
and does it have equal sign
and inequality.
No because this is an Open
Bracket.
Okay.
So that's the final answer
All right.
So now we can discuss deeper
about
this linear  inequalities
(*verbal typo :quadratic inequalities)
and question asks us to solve
so first
step rearrange and factorise.
Okay, so if we factorise that
we're going to get (2x+3)(x-1)
Okay.
So getting the value of x you
will get -3/2 and x=1
Okay.
So now
we are going to
fill in the table.
Okay, so,
okay.
So the first row release down
all
The factor
is so multiply them.
Okay, and we're going to list
down the
interval as well.
We know the interval is moving
from negative Infinity.
Until positive Infinity.
Okay.
So what is the number here
who comes first
obviously it is -3/2 and next is 1 so we're going to
put negative infinity and
-3/2 here
negative infinity, -3/2
also
here -3/2 and 1
also.
1 and infinity, so we already
know that Infinity always
open interval.
So Infinity always open interval
Infinity always open.
So what about negative three
over two and one?
Okay, let me draw a box here.
Okay, let's call it a blue box.
So look at this blue box.
Does the inequality have
equal sign
Yes.
So
it is a closed bracket.
What about the test value
We look at the easy part first.
What is in between here
between negative number and
positive number?
Obviously a 0 so we put 0 here.
What is a number of the one
obviously it's to you can put
90 95 100 199 if you want.
okay.
We know that negative 2 over 3
is
-1.5 so we can put -2
Okay.
So if we substitute -2, 0 and 2  in 2x+3.
Okay, so we will get a
negative number.
If you don't if you didn't
believe me, you can calculate
by yourself.
Okay, so multiply these two
signs
multiply negative negative you
get a positive
multiply positive and
negative will get negative
Multiply positive and
positive will get a positive.
Very good.
So
okay
within this one two three
intervals,
which interval.
is our answer look back
and I will blue box
that is it greater than 0 or
less 0
yes.
It is greater than 0 if it is
greater than 0 is it negative
or positive?
Yes, we want a positive
intervals,
but we have two positive
intervals.
Is it possible to get two
intervals as answer?
Yes, we can.
Okay.
So how to write this answer if
you have two intervals here.
Let me show you I'm going to
use black color this time.
Okay, so answer.
If you're going to write this
in interval form, okay, so
this is positive and this is
the interval
this is positive sign and this
is the interval.
So just
write down or just copy
the intervals.
And combine those interval using
the Union sign.
Okay.
So remember this always combine
intervals using Union sign.
Okay, and you're done.
Okay.
So write down the usual bracket
like that.
Okay,
so
negative Infinity to negative 3
over 2.
It is just x<=-3/2
It is just x=>1.
Why do I have an equal sign on
my inequalities?
Because negative 3 over 2 and 1
close bracket?
Okay.
So union the key word is it or
or and?
Yes, keyword for union is
or
and we done.
okay
if you didn't understand or
Or you didn't understand,
please, please please go
clarify with you
lecturer.
Thank you guys.
So next slide is the
Exercise.
Okay, so you can try this
exercise and check with your
lecturers.
The answers are there.
Okay.
Thank you so much.
Bye.
