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welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
make this into a 2 . make this into a 7 . negative times negative is positive . so you have 7 .
are you supposed to flip the negative sign when you make the reciprocal ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 're just left with an x equals 4 . i tend to focus a little bit more on this becaus...
how would you figure out x - y = -1 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do .
why do you have to flip the number 3/4 to 4/3 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do .
when you do the recipricol of negitive 3/4ths why is it still negitive ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do .
how does -3/4 simplify multiply by its reciprocal cancel out ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
why those equations are called linear ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
turn this into a 4 . make this into a 2 . make this into a 7 .
what 's a `` reciprocal '' ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
make this into a 7 . negative times negative is positive . so you have 7 .
is the x intercept equal to the y intercept times the negative inverse of the slope ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
make this into a 7 . negative times negative is positive . so you have 7 .
i thought when you do a reciprocal you take the negative sign off ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 're just left with an x equals 4 . i tend to focus a little bit more on this becaus...
when solving for the equation `` y= -1/3x `` and you are solving for y how would you plot that on a graph ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do .
why did n't you simplify the 3 and 39 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so we get x is equal to minus 40/39 . and i like to leave my fractions improper because it 's easier to deal with them . but you could also view that -- that 's minus -- if you wanted to write it as a mixed number , that 's minus 1 and 1/39 .
why do you switch fractions ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
turn this into a 4 . make this into a 2 . make this into a 7 .
what is the binomial that must be subtracted from 2a^2-5b^2 to get the monomial 3a^2 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so rewriting it , if i had 5x equals 20 , we could do two things and they 're essentially the same thing . we could say we just divide both sides of this equation by 5 , in which case , the left hand side , those two 5 's will cancel out , we 'll get x . and the right hand side , 20 divided by 5 is 4 , and we would hav...
do you always divide both sides of the equation by the same number ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
and i like to leave my fractions improper because it 's easier to deal with them . but you could also view that -- that 's minus -- if you wanted to write it as a mixed number , that 's minus 1 and 1/39 . i tend to keep it like this .
could you also simplify 3/39 to 1/13 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
for algebraic equations if the letter used to represent the factor or multiple , then why do teachers freak when you use 'the wrong letter ' ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
what is ure secret of teaching ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so this is just saying 5 times x , so instead of a question mark , we 're writing an x . so 5 times x is equal to 20 . now , most of you all could do that in your head .
if x= 1 1/20 , then how does 5 x=20 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
if you do that on the left hand side , we have to do it on the right hand side as well . minus 6/5 . the left hand side , the minus 6/5 and the minus 5/6 cancel out .
because 1/20=5/100 or 0.05 x 5=.25+5= 5.25 right ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
this becomes 4 . 7 times negative 3 is minus 21/20 . and assuming i have n't made any careless mistakes , that should be right .
what is the weight to the nearest pound of a person who is 64 inches tall and has a body mass index of 21.45 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular m...
if we are going to be using a dot for multiplication for now on instead of an x then why they do n't just teach us multiplication as a dot from the begining of first grade ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
if you said 5x equals 20 , instead of dividing by 5 , we could multiply by 1/5 . and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 'r...
how do u know when to split the # in half ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do .
wait , is n't the reciprocal of -3/4 +4/3 , not -4/3 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
and the right hand side , we have , well , we can divide both the 6 and the 8 by 2 , so this 6 becomes negative 3 . this becomes 4 . 7 times negative 3 is minus 21/20 .
if x is 4 and 4*5=20 , can you use variable in division ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so the coefficient , all that is , all that fancy word means , is the number that 's being multiplied by x . so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times...
say when you are doing the reciprocal of -3/4 should n't the negative sign be removed and it be 4/3 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
and the reason we do the notation a little bit -- we write the 5 next to the x , because when you write a number right next to a variable , you assume that you 're multiplying them . so this is just saying 5 times x , so instead of a question mark , we 're writing an x . so 5 times x is equal to 20 .
if 3x -1=11 , what is the value of x^2+x ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem .
a student pushes a box 5.0 m across the floor using a constant force of 20.0 n .how much work does the student do on the box ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular m...
why is the dot only used sometimes and other times not ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
actually , let 's do one of those right now . so let 's say i had negative 3/4 times x equals 10/13 . now , this is a harder problem .
why did n't you try to find the greatest common denominator of -4/3*10/13 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
make this into a 2 . make this into a 7 . negative times negative is positive . so you have 7 .
why does n't the 1 or 7 become negative when you simplify does n't the sign carry over ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do .
why does the 4 0ver 3 become a neg number ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
turn this into a 4 . make this into a 2 . make this into a 7 .
what is the solution when there are two variables , for example : 2 ( x-2 ) < 2/3 x p.s.- is there a video for those type of equations ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
make this into a 7 . negative times negative is positive . so you have 7 .
how do you divide a positive fraction with a negative fraction ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so the coefficient , all that is , all that fancy word means , is the number that 's being multiplied by x . so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times...
if the number is fraction with a negative ie ; -3/4 , should n't the reciprocal be 4/-3 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so 5 times x is equal to 20 . now , most of you all could do that in your head . you could say , well , what number times 5 is equal to 20 ?
could someone explain what a recprocle is ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
why is is linear , not just a regular equation ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 're just left with an x equals 4 . i tend to focus a little bit more on this becaus...
why can the 4 become a 1 and the 40 become a 10 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
how would you do a linear equation with fractions , decimals , negatives , positives , and percentages all in the same problem ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer .
what are systems of equation ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
did anyone else notice the mager change in font size ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer .
how do you write an algebraic equation when you are trying to find two numbers ; when you know their difference ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
let 's check to make sure that 's right . the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation .
what is the purpose of algebra and where in life will it be beneficial ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer .
how to write an equation in standard form ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 're just left with an x equals 4 . i tend to focus a little bit more on this becaus...
why did you need to divide by 1 over 5 to get 4 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
how do i apply systems of linear equations ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
you could work it out on your own to see that they do . they equal 1 , so we 're just left with x is equal to 10 times minus 4 is minus 40 , 13 times 3 , well , that 's equal to 39 . so we get x is equal to minus 40/39 .
why not reduce the 3 to 1 and the 39 to 13 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer .
is x = -2 considered a linear equation ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
how did human lifeform begin ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so you have 7 . 2 times 4 is 8 . and that 's what we said we would get .
my problem is -8 = y/-8 ( that 's y over -8 ) my problem is..i understand why y= - 64 but why does the book say it equals 64 ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
let 's check to make sure that 's right . the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation .
is algebra important in high school ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular m...
how can a dot mean times ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
how old is john now ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
when solving literal equations would i just replace the numbers with variables ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 .
where can find test problems for level 1 equations ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
how do you check equations when the variable is in a fraction ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
make this into a 7 . negative times negative is positive . so you have 7 .
my question is..when you do the recipricol of the first fraction , and the bottom denomenator is a negative , then why is it when you make it into a recipricol , the numerator becomes a negative ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
are linear equations always straight ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
well , we do the same thing . we multiply both sides by the coefficient on x . so the coefficient , all that is , all that fancy word means , is the number that 's being multiplied by x .
is it important to divide both sides by the no given on the numerator or we can just shift the numerator to the r.h.s ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular multiplication sign gets confused with the...
why does multiplying/dividing both sides of the equation with a ' # ' lead to solve a variable value ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
make this into a 7 . negative times negative is positive . so you have 7 .
why do you only use negative numbers when giving examples ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer .
what is the astigmatism of 8x-5xb if the linear equation of the equation is less than the mean of the solution ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
welcome to level one linear equations . so let 's start doing some problems .
so what does the repicle mean ?
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa...
so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular m...
i don '' t get how a dot can be times ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so this is the focus right over here . so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus . so that is the -- let me make it as close as possible .
0sal says the centre of curvature is twice the focus can anyone please prove it ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
which will be a pretty useful tool when we tackle other types of reflective or refractive devices like lenses . so that 's a parabolic mirror . i 've drawn its principal axis right over here .
does that mean that if you stood in front of a parabolic mirror in a fun house at the focus , you would see no image of yourself at all ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and so now the image is bigger than the original . so the image is real . and it is bigger .
when the object is in front of the mirror you get a real image , now why i see the reflexion in the mirror ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and the reason why i want to do there is because there the parabolic mirror is essentially flat and essentially vertical . so you can imagine that the incident ray is going to be the same thing as the reflected ray . so you could draw a ray that comes in like that .
if an incident ray were to go through the center of curvature , would it 's reflected ray go directly back along the same path it 's incident ray took ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus .
what exactly is the center of curvature ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
these lines are the hardest thing to do . so parallel incident ray , parallel to the principal axis . this is the principal axis right here .
however , what if you drew the ray downwards , towards the very center of the parabolic mirror and have it reflect on the principal axis ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus .
what is the centre of curvature ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
let me do another example like that where i do something big way out here just to make it clear . so once again , we go parallel , reflect through the focus . and then , we can go through the focus .
why do all the reflected rays of the rays parallel to the simmetry line go through the focus ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and i 'll just do it for this one right over here . it will reflect through the focus . and then , if you have something that goes through the focus , an incident ray that goes through a focus , it will reflect parallel .
i mean , how do rays reflect in a paraboloid surface ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
but they look like they 're diverging from some point behind the mirror . they 'll look like they 're diverging from some point behind the mirror . so in this case , we are forming a virtual image . and the virtual image will actually look something like this . and so it 'll be larger than the original virtual image . ...
`` 5 '' can the virtual image be smaller or equal to the object ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so here , i 'll do a slightly different ray . i 'll do a ray that intersects the parabolic mirror right over there . and the reason why i want to do there is because there the parabolic mirror is essentially flat and essentially vertical .
for the fourth ray diagram sal could use another rule or we can say a property of parabolic mirrors that is a ray passing through the centre of curvature pass through the centre of curvature itself ... ..so instead of drawing a ray from the pole ( that is on the point on the principal axis that intersects the parabolic...
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so this point will correspond to this point over here . i think that makes it clearer , that this image , the image of this object when it 's reflected by this parabolic mirror will look just like that . so it will actually form a real image .
what will be the characteristic of the image formed if the object is placed at infinity , from the mirror ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so you could imagine coming from the same direction as the focal point would be reflected parallel , in a parallel direction to the principal axis . now , these two light rays are not converging . but they look like they 're diverging from some point behind the mirror .
does the information remain constant for the two ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
they 'll look like they 're diverging from some point behind the mirror . so in this case , we are forming a virtual image . and the virtual image will actually look something like this .
in the case where the object is placed at the focus , the rays go parallel forming no image , but if we have a converging lens , as in the case of our eyes , what will be the effect ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
it goes through another ray . it goes through the focus . and then , it reflects .
is there any difference between the focus and the principal focus of a mirror ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and so now the image is bigger than the original . so the image is real . and it is bigger .
can the real image be slanted ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
which will be a pretty useful tool when we tackle other types of reflective or refractive devices like lenses . so that 's a parabolic mirror . i 've drawn its principal axis right over here .
what is the difference between a concave and parabolic mirror ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors .
i understand how images can appear in different sizes and in different orientations but do parabolic mirrors also distort the image ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so it will actually form a real image . it 'll form a real image that is smaller than this original image . it 's not so clear , the way i did it over here .
that is to say , does the reflected image appear to have different proportions rather than just being scaled ( up or down ) or flipped ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and so now the image is bigger than the original . so the image is real . and it is bigger .
so a real image is formed if the light rays intersect ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus .
is center of curvature the same thing as the radius of curvature ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
you might want to pause the video and try it on paper because really nothing beats practice . so let 's stick our object between the center of curvature and the focus and the focal point . so if we put our object there , we could have a light ray that goes parallel to the principal axis .
can anyone tell me briefly about centre of curvature , focus or focal point and principle axis ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and it 's not , it does n't look like it 's diverging from some point in the mirror . so it wo n't even form a virtual image . so here , there will actually be no image when the object is actually at the focal point .
is it possible to see the magnified virtual image ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so let 's stick our object between the center of curvature and the focus and the focal point . so if we put our object there , we could have a light ray that goes parallel to the principal axis . and then , it will reflect out through the focus .
why is the object put on the top of the principal axis ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so here the image , just so we can keep track of things . here , the image is real and smaller than the actual object when the actual object is beyond the center of curvature . and actually , let me make it a little bit clearer by drawing .
why is an image smaller when the object is much behind the center of curvature ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
which will be a pretty useful tool when we tackle other types of reflective or refractive devices like lenses . so that 's a parabolic mirror . i 've drawn its principal axis right over here .
just a quick question , is the center of curvature always twice the focus in a parabolic mirror ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
let me do another example like that where i do something big way out here just to make it clear . so once again , we go parallel , reflect through the focus . and then , we can go through the focus .
is there any way to geometrically prove that the rays from an object at the focus will emerge parallel to each other after reflection ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and the convention is to use an upward pointing arrow . this is n't a light ray . it 's used to show an object .
does the light ray that had hitted a body carry the information about the body that it has hitted ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and then , a ray that goes through the focus will be reflected out parallel . it would be reflected out parallel . and at least for the light that comes from that tip , they will re-converge at that tip .
so do the photons of light carry information about the part from which they are reflected ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so in this case , we are forming a virtual image . and the virtual image will actually look something like this . and so it 'll be larger than the original virtual image . so it 's kind of a magnifying .
why , when the arrow was drawn at the focal point , there could n't have been a ray drawn like it was drawn ( the second ray ) ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus .
what is the center of curvature ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and so now the image is bigger than the original . so the image is real . and it is bigger .
can someone please explain the differences between a real and a virtual image ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors .
are convex and concave mirrors parabolic mirrors ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
and anything that , any light that goes parallel will then look to come out in a direction that would go through the focal point . so it would go through the focal point . it would come out in that direction .
what would we exactly see if the object were at the focal point ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors .
so , will the screen remain dark ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
these lines are the hardest thing to do . so parallel incident ray , parallel to the principal axis . this is the principal axis right here . principal axis -- that 's what this line is right over here .
how do you determine the image location of an off axis parabolic reflector , when you are viewing it at 90 degrees relative to the parent parabola 's central axis ?
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi...
so it will actually form a real image . it 'll form a real image that is smaller than this original image . it 's not so clear , the way i did it over here .
when the image is in front of the focal length , the image that is projected , is it larger or roughly the same size as the object we have ?