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How To Solve One & Multi Step Equations & Variables
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Feb 19, 2025
In this chapter, we'll learn about solving one and multi step equations, and also learn how to solve for variables. But prior to that we'll be discussing some key properties of real numbers that actually will be very handy in the process of solving equations. Chapters: 00:00 Intro 00:27 Reflexive Property 01:34 Symmetric Property 02:26 Transitive Property 03:09 Substitution Property 03:52 How To Solve 1 Step Equations 06:49 How To Solve multi step equations 08:19 How to solve for variables 11:48 Working on examples
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0:01
all right so we going to talk about uh
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the properties of equality okay when it
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comes to now this is just for real
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numbers all right real numbers Encompass
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all the numbers which is rational
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irrational uh whole numbers natural and
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decimals so all of that is encompassed
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in here so we're going to just learn
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some quick properties they're not hard
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to understand okay the first one is what
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reflexive reflexive a is equal to a
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just like that right so x + 12 = x + 12
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3 is = 3 5 is equal to 5 -2 is equal to
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-2 that's called a reflexive property
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meaning a number is equal to itself it
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does not change sh is equal to
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shape it doesn't change so it's a
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reflexive reflexive meaning you are who
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you are you are yourself right so x + 12
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is = x + 12 a is equal to a that's a
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reflexive oh property if you look at at
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yourself in the mirror you don't change
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do you no
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I well it depends when you have your
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real mirror when you drive a car that's
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different you change sh what what do you
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see when you see yourself in the mirror
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what do you see
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the next thing the next next property is
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called the symmetric like symmetric so B
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basically if a is equal to B then B is
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equal to a does that make sense right if
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I give you an example here 18 = -2 n + a
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that means -2 n + a = 18 it sounds
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almost like the commutative law where
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you can switch things around if a is
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equal to B then B is equal to a so if I
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have
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if x is equal to
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Y then likewise Y is equal to what x
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meaning you can switch it it does not
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change the equation does that make sense
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right 5 x + 5 is = 3 I can also say that
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3 is equal x + 5 okay so that does not
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change uh the equation all
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right next transitive the transitive law
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is also interesting so basically if a is
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equal to B and B is equal to C then a is
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equal to
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C right so let's let me give you an
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example if x + 1 is = to 2 Y and 2 Y is
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equal to 5 then I can conclude that what
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x + 1 is also equal to 5 does that make
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sense you it's called a transitive law
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so if one is equal to the other and the
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other is equal to another thing then the
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primary can also be equal to the
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tertiary right the third one all right
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so that's just called the transit now
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substitution substitution is really easy
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stuff so if a is equal to B then a may
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be replaced by B and vice versa right if
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I have an equation let's say I have 2 x
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+ 5 = to um three and I say let x equals
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to two then I can replace the two in
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here right that means 2 * 2 + 5 is equal
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3 obviously that's false because that's
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not how it is but you understand what
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I'm trying to say you can substitute a
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number by something else if you're given
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a value for it so that's the
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substitution okay now the very next
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thing that we going to discuss is
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solving one step equations One Step
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meaning it requires literally one step
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right and I'm sure you guys did you guys
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did this in
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pre-algebra algebra one and now Algebra
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2 it's the same thing that's going be
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itself even until we go to Calculus if
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you are in calculus
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right
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so K how you going to solve this so you
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have x - 3.24 this is a decimal number
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right it's not three times it's
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3.24 equals to 42.1 how do you solve
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this um you subtract it by the other
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side you which one are you solving for
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well you would well technically you
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change your yeah that has to move right
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yeah since this is subtraction what do I
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do to get rid of this we make it
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positive positive right I'm going to add
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3.24 right
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3.24 now we don't need the calculator
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for this so we got four 3 5 so X is
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equal to 4534 again this is very basic
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stuff okay
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now some of these are a little confusing
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yes sir wouldn't that be
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4535 no 34 because this is a zero
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here all
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right 42.1 is 4 is
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42.1 plus
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3.24 right you assume that there's a
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zero
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here all right so it's 4534
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all right now the next one is a little
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more complex so we have
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-5 over
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8X equal to 20 so how do I solve this by
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using one
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step
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go uh you multiply those by 8 or 8 overg
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five yeah that's right cuz I want to get
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rid of this so I want what what do we
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call that it's called the start with r
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right re see reciprocal right so you
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times this by 8 over5 and then you do
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the same thing
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here right and now you can solve this in
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one step we're done because this is
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going to cancel this and this is going
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to cancel this so you're left with X and
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then 20 * 8 over 5 we can simplify that
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right again we never leave
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fractions we always have to simplify
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fractions right I know that five goes
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into 20 how many times four four and
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then it's four *
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8 what does that give me
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322 32 right so this should be 32 again
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this is like one step in one step you
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can solve these equations all right so
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these are called one step equations and
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then we're going to jump into the
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more uh complex equations which are the
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two steps or multistep equation can I
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erase this no all right go
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ahead you good good all right
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so
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here how do I have solve this equation
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you have 5 par x + 3 + 2 1 - x = 14
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distribution distribution all right so
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how do I do that distribute 5 into and
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all right and
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then all right so that gives me what 5 +
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15 okay plus
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2 - 2x mhm = 14 all right so what's the
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Next Step once you get here combine like
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things combine like things so what about
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combine the two the -2X and the 5x what
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is that going to give me 3 3X 3X and
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then what else and then the 15 and the
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two that gives me 17 right and then we
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out that then what's next- 17 and 14 -
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17 right and we get 3x
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= 33 and then last step
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right three three right so that's
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xal
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negative one all right right negative
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one uh now the the next one is a little
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more complicated it is not hard it's
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just a little more complicated here what
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we have and what did he say solve for
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what variable right so we don't have
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numbers and sometimes people get a
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little hung up on that well this is too
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much so how would I solve for
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H yes sir get it get it on time yeah so
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how would I do that distribute it
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distribute it would I be a good idea if
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I distribute it no right cuz it's going
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to give us more work to do right so what
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we need to get rid of first to make this
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simple no I'm trying to solve for H
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parentheses pares right so how about I
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get rid of that add those together them
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we can't add them cuz they're not like
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them it's B1 plus B2 so there's nothing
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I can do no that sounds good but no we
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can't right so that's the formula for
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what what's what's what formula is this
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no Circle no trap trape right so we
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trying to Sol for H so what what's the
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easi to move out we can move this by
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what operation yes sir um we want to um
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divide divide right we're dividing so
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I'm going to divide this by B1 plus
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B2 and why am I dividing and not adding
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or subtracting why um multiplication
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because it's a multiplication right so
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this imply a multiplication that make
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sense yes no no but I don't we go over
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it again is that b sub one and B sub
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yeah that's B sub one and B sub two so
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basically why would you do that all
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right cuz this is 1 12 H V1 plus V2 what
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I don't have anything in between these
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numbers right yeah so that implies the
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multiplication so this is 12 * h * B1 +
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B2 so I want to solve for H right I want
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to get this by itself I want this to be
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by itself so I have to get rid of this
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first step but because this is a
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multiplication you do the opposite oh
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okay that makes sense so therefore now
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you divide it right so I'm going to
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divide it I'm going to
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divide and now this is gone right so I'm
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going to rewrite this whole operation so
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I have a over B1 Plus 2 = 12 and H right
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so now how do I get rid of
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the2 yes reciprocal reciprocal so what
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would be the reciprocal here two 2 over
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one right so I times you by 2 over one
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and guess what I have to do the same
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thing here right 2 over one so now this
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is gone so now I have h = 2 a over B1
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plus B2 and that's it leave it like that
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you leave it like that there's nothing
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El we can do here is anything El we can
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do here no no we can't samplify we can't
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do anything else so we leave it like
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this so I'll give you a couple of things
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to work
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on to make sure we understand this so
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let me find it in the book
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do I want you to
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solve uh
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that's one two eight
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all
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right so go ahead and solve these two so
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first solve for H knowing that um s = 2i
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r² + 2 pi r h i want you to solve for H
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and here if 6x - 12 is 18 I want you to
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find the value of 6X +
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5 okay
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we don't need to record anymore we
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good yeah
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