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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