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hello this is mr. Buffington and today
we are going to solve for that variable
of X and one-step equations to do this
we need to remember inverse operations
inverse operations or opposite
operations are the operations that undo
each other addition is the opposite of
subtraction multiplication is the
opposite of division we're going to see
this again and again and again in all
the examples that we do today we need to
remember that that those are opposite
operations now let's start solving to
solve for a variable of X when you're
given an equation like this you have to
follow three steps I know you can look
at that and probably tell me that three
plus two is five but we're going to
follow the same steps every time and
you'll see that if you know these steps
it'll make it easier when the equations
get a little bit more difficult step
number one find the variable our
variable is X the next step is to say
what happened to X or what is attached
to X in this case what's attached to X
is plus two that's what we're doing to X
we're adding two so now is when we need
to know that inverse operation what's
the opposite of adding two well its
subtracting two we know that addition is
opposite of subtraction so we are going
to subtract two from both sides of the
equation that keeps the equation
balanced so on our left side we have X
plus two minus two which gives us just X
by itself and on the right side of the
equation we have five minus two which
gives us three there we go
X is equal to three three plus two is
five and we're going to follow these
steps for all the rest of the questions
that we do let's look at a question
involving subtraction same steps find
that variable our variable in this case
is X what happened to X or what is
attached to X
well we have X minus seven good so let's
do the opposite of minus 7 to both sides
of the equation in other words instead
of subtracting 7 we are going to add 7
to both sides of the equation X minus 7
plus 7 leaves us with X by itself on the
left side and on the right side we have
12 plus 7 12 plus 7 is 19 we're able to
solve the equation you can check your
work now look at the top is 19 equal to
X does X minus 7 equals 12 or in other
words does 19 minus 7 equal 12 you check
your work you'll find that that is
correct now we're going to look at a
question with division a good thing to
do about this time is to pause the
recording and try one of these on your
own
following the same steps here's what we
do find that variable in this case our
variable is n it doesn't matter what
letter you use you can put any letter in
there we used n this time what happened
to N or what's attached to N divided by
3 and divided by 3 so what is the
opposite or the inverse of dividing by 3
multiplying times 3 is the inverse so
now what we will do is multiply times 3
on both sides of this equation notice I
use the dot to represent multiplication
that's common you'll see that more and
more as you get into higher levels of
math classes so n divided by 3 times 3
leaves us with just n on the left side
and on the right side of the equation we
have 71 times 3 which gives us 213 for
our final question we are going to use
the equation 5y is equal to 30 step
number 1 find that variable in this case
the variable or the letter that we're
using is why step two what happened to
why we just have 5y written there
it doesn't say 5 minus y or 5 plus y or
5 divided by y when you have a letter
next to a number like that it implies
that you are multiplying so what
happened we multiplied times 5 so let's
do the inverse or the opposite of that
and divide by 5 so we're going to do
that on both sides of this equation 5y
divided by 5 leaves us with just Y on
the left side and 30 divided by 5 will
go on the right side of the equation 30
divided by 5 equals 6 so that's the
final solution for the variable in this
equation as you're looking through this
and remember the steps to find the
variable asked what's happened or what's
attached to that variable and then do
the inverse or opposite operation to
both sides of the equation I hope this
lesson was helpful for you and have a
wonderful day
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