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Homeschool 8th grade math



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hello John Zimmerman from tabla class

calm and what I want to do here is help

you out by solving some basic equations

and these are our first set of problems

there's other videos that we're going to

go over so this is our first set we're

going to look at and if you can solve

these then then you'll be well on your

way to solving more sophisticated

problems so let's take a look at our

first problem here that's 2x equals 10

okay this is 2 times X equals 10 and the

objective when you're solving an

equation is to get x equals and then

whatever that number is going to be is

the solution ok so the way we do a

problem like this ok because we have 2

times X what we want to do is divide

both sides of the equation by 2 okay is

2 divided by 2 is 1 or we could just

write this way 1 X or simply X okay now

if I divide the left-hand side of an

equation by a number that's okay I just

have to be fair and do the same thing on

the right-hand side so here I have 10

divided by 2 and that is 5 okay so I

have 1 x equals 5 more commonly we just

write it as x equals 5 and this is our

solution okay all right so let's take a

look at our next problem here I have Y

minus 3 equals 12 so to solve for that

ie get Y by itself on the left hand side

of the equation what I need to do here

is add a 3 okay so if I add a 3 to the

left hand side and add negative 3 and

positive 3 I get 0 or I'm just left with

Y by itself okay so I have to add to

both sides of the equation and that's

the key concept here

whatever you do in key concept in

solving an equation whatever you do to

one side of an equation you have to do

the right to the other okay so it's this

whole idea of balance ok so now I'm

going to do is just add down alright so

I get Y plus nothing is y and negative 3

plus positive 3 is 0 and 12 plus 3 is 15

okay so there you go y equals 15 now

let's cut take a look at

so I'll leave this problem here for last

let's look at this next one Z plus 6

equals negative 3 ok same concept here

if I want to get Z by itself to solve

the equation this time I have to

subtract 6 from both sides of the

equation by the way notice how I'm

working this is really important you

want to show all your steps for a

variety of reasons but nevertheless if I

subtract 6 from the left-hand side I got

to do it from the right-hand side and

now I'm going to add down ok and I'm

going to get Z alright this positive 6

plus negative 6 is 0 that goes away and

then let me ask you what's negative 3

plus negative 6 that's negative 9 and

the reason why I kind of ask you that is

it's another area where students get in

trouble with when they're solving

equations they don't know they're

positive negative rules or there are

rules of integers and you know they

struggle with you know adding positive

negative numbers on top of trying to get

the concepts down for you know solving

an equation so you really want to make

sure that you go back and take a look at

positive negative number rules if you're

struggling same thing with fractions and

speaking of fractions take a look at our

last problem so I have 1/3 x equals 5 so

when you're dealing with the fraction

what you want we want to do to get rid

of it ok a fraction coefficient a

fraction front of the variable remember

the objective is to get 1x or X by

itself so you just go ahead and multiply

both sides of the equation by the

inverse and all the inverse is or the

reciprocal excuse me is taking this

number okay this 1/3 in front of the X

and flipping it around okay so when I

flip it around it's called the

reciprocal so now I'm going to multiply

both sides of the equation by the

reciprocal and take a look at what

happens I got 3 over 1 or 3 okay so 3

times 1/3 is what now to think about

that 3 times 1/3 is 1 okay or 1x so

that's what I want then I have 5 times 3

over 1 or 5 times 3 that's 15 so you get

X is equal to 15 okay so you have to

master these basic

equations before you move on to more

sophisticated equations but listen I

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right keep working hard and check out

some more videos and if you don't mind

can rate this video if you have some

time good luck