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>> This is YourMathGal,
Julie Harland.
Please visit my website
at yourmathgal.com,
where all of my videos are
organized by topic.
This is Video 7 in our series
of videos on Solving Equations
with Parenthesis.
So, let's try this one.
You could do it
on your own first
and then come back
and see how you did.
All right.
So, what we need
to do is simplify each side.
So, on the left hand side
here, we're going to have
to distribute our 4.
So, we have 4 times 2X,
that is 8X.
And then 4 times negative 3
or you could give this minus 4
times 3 is negative 12
and then I've got this
minus 5X.
And on the right-hand side,
we're going
to do the distributive
property as well multiplying 3
times X which is 3X,
and then minus 3 times 4,
that's 12.
And then we want
to simplify each side,
the right-hand simplified,
but on the left-hand side,
we have an 8X and a minus 5X
for like terms.
So, that's a 3X minus 12
equals 3X minus 12.
And right here,
we can see
that this is an identity.
It has the same exact thing
on each side.
That means regardless
of what we put in for X,
we'll have a true equation.
So, the solution--
I'm not writing very
well here.
[ Pause ]
You could write all real
numbers if we're talking
about real numbers,
which usually, you could put
that in a solution set
or real numbers.
There's all sorts
of different ways to write it.
Some people write it
like that.
That's another way.
So, all of these are ways
of writing that answer
and it's an identity.
All right.
Now, you may wonder,
well how do I know
for sure it's identity?
One way to do it is just go
ahead and put any number
in for X and see if we get
through the same number
on each side
when we simplify it
and then put another number
in for X and see
if that happens.
If it happens twice, well,
you've certainly found,
you know, just randomly two
numbers are going to work.
It looks pretty good
that all real numbers is
probably correct.
So, let's do that.
All right.
So, pick any number you want
for X. Plug it in for X
on the left-hand side,
simplify it,
plug it on the right-hand side
and simplify it,
and make sure you get the same
number on each side.
Okay. So, I imagine, you know,
there's, you know,
thousands of possibilities
somebody might try.
I'm going to try an easy
number like, you know,
I could try zero
or I could try one,
or I could try two.
You know, those are pretty
numbers, pretty easy numbers
to plug in.
I could plug in ten.
It's really up to you.
So, how about if I just plug
in zero?
That's a really easy number
to plug in.
Okay. So, I'm going
to plug in 0, 4X.
[ Pause ]
And I'm going
to do a left-hand side.
So, in this parenthesis,
I'm going to end
up with 0 minus 3
which is just negative 3,
and minus 5 times 0 is just 0.
So, this just becomes negative
12 minus 0 or negative 12.
I'm showing every single step
here because, you know,
hopefully, you're okay
with that not writing negative
12 minus 0, but you could do
that as well.
And over here, we're going
to put in zero for X.
And I'm going to get 3 times--
well, 0 minus 4 is negative 4
and I do get negative 12.
So, it certainly checked
when I plugged
in X equals zero.
Let's just plug
in another number.
So, we'll take the same
equation, 4 times 2X minus 3
minus 5X and 3 times X
minus 4.
And let's go ahead
and just plug
in any other number in.
How about--
let's check,
how about X equals--
I don't know.
How about 4?
How's that?
So, we will plug in 4 for X.
[ Pause ]
And we'll just simplify this
left-hand side.
So, that's 8 minus 3
in parenthesis
and 5 minus 4 is going
to be 20, like this is 4 times
5 minus 20.
So that will give me 20 minus
20 which is zero.
So, on the left-hand side,
I ended up getting zero.
Okay, let's see what's happens
on the right-hand side.
I'm putting in 4 for X, right?
Now, I did this
at random, you know?
I didn't know
that this is going to be zero,
but it doesn't really matter.
The point is,
do you get the same number
on each side?
No matter what number you put
in and actually you will.
So, you might have tried X
equals 1, X equals 2,
X equals 1/2,
X equals negative 9.
Up to you,
there's infinitely many
possibilities to try.
So, that looks
like our solution up here.
Let's correct.
All real numbers.
And usually in books,
they don't check it
but you can always check
to make sure you got an
identity just
by trying a couple
of numbers in there.
This is YourMathGal,
Julie Harland.
Please visit my website
at yourmathgal.com,
where all of my videos are
organized by topic.