Tip:
Highlight text to annotate it
X
>> This is YourMathGal,
Julie Harland.
Please visit my website
at yourmathgal.com where all
of my videos were organized
by topic.
This is video 2 in our series
of solving equations
with grouping symbols
such as parenthesis
and brackets.
In fact, we have both of them
in this particular equation.
So, we began solving equations
by simplifying each side.
So, on the left side,
we know-- we see we have
parenthesis so we're going
to have to do the distributive
property here.
So, that's our first step
over on the left side,
is to distribute that 2
so that we have 2 times 5
which is 10 minus 2 times 3X
which is 6X.
And then on the right,
you have to be careful here.
It is true there's a 5
and there's a bracket instead
of parenthesis and that's
because there are parenthesis
further inside.
So, what we want
to do here is we want
to simplify on the inside
of those brackets as much
as possible before we
distribute that 5.
That isn't the only way
to do it but I think it's
easier for most people
so let's do it that way.
So inside, I'm going to have
to distribute this 2
and it's really a negative 2,
right, to the X
into the negative 2,
so I'm going to just copy
up through there
and now I have negative 2
times X, that will be a minus
2X and I've got a negative 2
times a negative 2 really,
ends up being a plus 4.
And notice,
I haven't simplified
within the bracket yet,
so I'm just going
to copy the left hand
side here.
Now, since there are no more
parenthesis,
instead of writing brackets,
I could just change and write
that grouping symbol
with parenthesis.
You could keep it as brackets
if you want.
In fact these brackets could
have been parenthesis,
but it sort
of helps people keep track of,
you know, what goes
together where.
So, if we combine
like terms here,
I've got 2 plus 4 that's 6
and then I have the minus
2X still.
So, I still have
to simplify the right hand
side by doing the distributive
property with the 5 now.
So, I still have 10 minus 6X,
now I have 5 times 6 is 30
minus 5 times 2X is 10X, huh.
Okay, I finally got rid all
of those grouping symbols
and now I'm
down to solving an equation
where I've got variables
and constants on each side.
How about we put the constants
on the left hand side,
so I'm going to add 10X
to both sides.
[ Pause ]
And so, I'm going to--
how about subtracting this 10
so I have the constants
on the right hand side.
So, I'm adding a negative 10
plus 10X to both sides
of the equation.
So, over on the left hand
side, I'll end up with just 4X
because negative 6 plus 10,
you're just going
to add those coefficients
as 4X and on the right hand
side, they have 30 minus 10
equals the negative 10X
and plus 10X is 0, right?
So, I get 4X equals 20.
All right, so,
and we're almost done.
Just divide both sides by 4
and it we end
up with X equals 5.
Now, I said at the beginning
of this, you could distribute
your 5 first.
So, I'm also going
to show you how to do it
that way, but I'll do
that at the end of the video
for those of you
who don't want to know,
just want to go ahead and do
with the innermost grouping
first, the distributive
property in the inside first
which is the most common way
of doing it.
So, let's go ahead
and check this answer,
X equals 5.
[ Pause ]
All right, so, we're going
to check 5 so we're going
to replace X with 5.
So, instead of X there,
I'm going to put times 5
and I'm going to simplify
within the parenthesis first,
right, because now we're just
simplifying this expression
and so inside the parenthesis,
I have to do this
multiplication first.
Do not divide minus 3 first,
okay?
Multiplication before
the subtraction.
So I have 5 minus 15
which if it helps you,
you could think of that
as 5 plus a negative 15,
that's up to you,
and within parenthesis I'm
adding a positive
and a negative number
and there's more negative
so it's negative 10, right?
We have 2 times negative 10,
positive times negative is
negative so I get negative 20
on the left hand side.
Okay, now let's work
on the right hand side.
So, we're going to start
by just copying everything
but plugging in 5 for X
and now we're going
to simplify this by working
within the innermost
parenthesis first.
No distributive property,
right?
So I have 2 minus
2 parenthesis.
What's 5 minus 2, 3.
Okay, now I have to simplify
within these brackets still
and I've got this
multiplication, It's 2 time 3.
Make sure again,
you don't do 2 minus 2 first,
you're doing order
of operation,
that's multiplication,
multiplication
before subtraction.
So, I could keep this
as a bracket
or I could do it parenthesis.
I'm going to keep a bracket
for a moment, that's 2 minus 6
and now I'm going
to just put a parenthesis.
You could keep it
as a bracket,
it doesn't matter.
All right, 2 minus 6,
you could think
of this 2 plus negative 6
and so writing a positive
and a negative number
so there's more negative
so we're going
to have negative 4.
And then 5 times negative 4 is
negative 20,
so that's the check
looks like.
I think it might be longer
to check than just do the
problem over.
It checks,
so this is the correct answer,
so our solution if we want
to write it
in braces would be 5,
that would be the solution
to that problem.
All right, for those of you
that are still with me,
I'm going to show you how you
could distribute your 5 first,
but you got
to be really careful here.
So, on the left side,
we could still do the
distributive property,
get the 10 minus 6X,
but when you distribute the 5
here, you got to be careful.
There's only really two terms,
the 2 in this whole thing
over here is another term
so when you distribute,
you're just distributing
to that whole term
right there.
So that will give you 5 times
2 which is 10
and then you have 5 times this
stuff so you're just doing the
5 times 2 first and 10
and just write
in the X minus 2.
You have to be careful,
you don't put in extra 5 times
that X minus 2.
So, as I said this could be a
little more confusing,
distributing the 5 first.
It is not the way it usually
taught, but I just want
to show you
that if you're careful,
you could also do that.
Now, we're going
to distribute the minus 10
so it's a negative 10X plus 20
and the rest
of it begins looking
like our other problem,
10 plus 20 is 30 minus 10X
and from here,
it looks exactly
like the other problem we did
before we finished
the problem.
So, I'm going
to finish this quickly.
We just add the 10X
to both sides
and we subtract the 10
to get 4X equals 20
which also gives you the
answer of X equals 5
which we already checked
and know that's the
correct answer.
So, that just gives you an
alternate way.
I don't suggest
that you do that.
I think it's better to work
within parenthesis first,
but I'd like to show
that there's always more
than one way to go
about solving a problem.
This is YourMathGal,
Julie Harland.
Please visit my website
at yourmathgal.com where all
of my videos were organized
by topic.