First-degree equations with
fractions and parentheses. Boys and
How are you girls, welcome to the
math channel with John and we're going to
solve this equation where you have to
to be very careful with this sign
less that affects the parentheses, it's about
of a first degree or degree equation
1 with fractions and parentheses. Before
throw ourselves like crazy to solve this
first-degree equation we have to
understand what solving an equation is,
what we're doing when we say
"we're going to calculate the solution of a
first-degree equation." Well, we have
to know the following. First we have
to know that there's some kind of function
which are called linear
and this is the general form of a
linear function. These linear functions
have a very nice property and is that
if we represent them on the plane
Cartesian it turns out that they are always
straight lines, are straight lines, lines
that can be in many ways.
It may be so, it may be so, .... Well look,
I'm going to draw one, specifically this one.
This is a straight line,
is given by a linear function and look,
this straight line against the x-axis.
at this point. Well, guys, it turns out
that linear functions can be
equal to zero. Look, this function
I'm going to equalize it to zero.
Solve an equation, an equation of
degree one, is to calculate this point of
cutting, the cutting point on the axis of the
"x", at which point the function cuts off the axis
of the "x's." This is really what
means solving an equation of
first grade and we're going to solve
an equation right now of the first
degree, that is to say, we what we are going to
to do is to find out at what point the function
next, at which point the function
next (x, two, minus one third less
3x, 6, minus 1 match of 12) at what point
This function shortens the "x" axis.
and let's go, let's go for it, let's go
solve it, we're gonna solve it. What's the point?
Point will it be? At what point will it be? At what point will it be?
point will cut this function to the axis of the
"x"? We just saw the preamble more
important, understand the problem well.
Now we're gonna figure it out, we're gonna
solve it. Come on, guys.
Before we solve we have to look at a
little, to study a little this equation of
first degree, linear equation and so
we see that, boys, girls,
this can be simplified. Do we have three
sixths? This equation can be ... three sixths
we can write it as... if we divide it.
up and down by 3, dividing up
and down between 3
we're going to have that this fraction is
equivalent to this one. Yeah? If we split up
up and down between 3 we have this. Okay.
Well, a half, a half. We rewrite this
equation of the following, of the following
way: "x" means minus one third minus "x"
means equal to 1 game of 12. Good!
Our next step is to remove this
parentheses. A lot of care, a lot of care
watch out for this minus sign because this
less sign affects the signs that there are
within the parentheses and a super error,
but super typical, go here to see
the most important errors of the
mathematics,
a super typical mistake is to do what
next: "x" means minus one third less
"x" means 1 match of 12.
Guys be careful because these are no less,
this is more, because less for less is
more and I'm going to put here the sign implies,
pardon, the equivalent sign
and we go on, we go on. Here we have our equation,
our equation a little more
simplified and we see that we have
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fractions, we see that we have fractions.
Ah, look! We have here "x" means and here "x".
means. "x" means plus "x" means, this such
time we could write it from the next
way: then "x" means plus "x" means
(we can write it that way, of course)
minus a third equal to 1 match of 12,
that is to say, 2x party of two, minus one
third and this would be equal to 1 game of
12. 1 game of 12. We can simplify
here, here we can simplify 2 above 2
downstairs. We simplify and this is
equivalent to "x" minus one third equal to
1 game of 12.
Well, well, well, well, well, well, well.
Ah, look, look how beautiful! The "x" the
we're almost, almost ready to be
clear. Look, we have the "x" minus one
third. Boys are less than one third that
there is here I can make you the following
play, I can add here a third and
add here a third, whatever you do in a
member I do in the other, this is the
game that is always done with the
equations and doing this little game,
minus one-third plus one-third we are
would go, this would go away and we could
write, we could write that
"x" is equal (let's put the east sign of
equivalence) "x" is equal to 1 match of
12, 1 match of 12, plus, plus
A twelfth plus a third? I am
to do up here.
A twelfth plus a third, look.
we could make the least common multiple
of 12 of 3 and blablabla.
To trade fractions using minimum
common multiple go to this video, but I
here I'm going to do something else, here I'm going to
to do something else. I'm going to do it
understanding a little the handling of
fractions. Look, I want these two
fractions have the same denominator.
What can I do to make this fraction
has the same denominator as this one? Well
what I can do is this: I can
multiply this fraction by this one,
4 out of 4.
And doing this little trick, doing
this little trick just watch what happens.
This is what happens.
I happen to have 1 game of 12 + 4 by
one is 4 and 4 by 3, 12. Ha, ha! Now I have
the same denominator, then this is the same
a
5 games of 12. Little friends, little friends.
little friends, I can write that this is
equal to 5 games of 12. And colorín
colored
the equation is over. The one who
solution of this equation is "x" equal to
5 twelfths means the following:
means
the function associated with this equation is
i.e. the function
x means less than one third less 3x
match of 6 minus one twelfth
this linear function, it turns out that
I don't know how, how it's going to be (this is
a straight line) I don't know how it's going to be
oriented, but I know that
is going to cut the x-axis in a
period. Well, this point is going to be worth
Five-twelfths. This is what it means
solving a first-degree equation is
say I'm calculating for which values
it is fulfilled, it is fulfilled the following, that
"and" equals zero.
Good friends good friends we have
at the end of the exercise, I say goodbye to
you. Perhaps you would like to subscribe,
then subscribe, subscribe. You
many more videos on this topic. Please
next video. Come on, see you soon.
Goodbye!
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