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

saying 5 times question mark equals 20. 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. Now, most of you all could

do that in your head. You could say, well, what

number times 5 is equal to 20? Well, it equals 4. But I’ll show you a way to do

it systematically just in case that 5 was a more

complicated number. So let me make my pen

a little thinner, OK. 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 have solved it. Another way to do it, and this

is actually the exact same way, we’re just phrasing

it a little different. 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’re just

left with an x equals 4. I tend to focus a

little bit more on this because when we start having

fractions instead of a 5, it’s easier just to think about

multiplying by the reciprocal. 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. I can’t do this one in my head. We’re saying negative

3/4 times some number x is equal to 10/13. If someone came up to you on

the street and asked you that, I think you’d be like me,

and you’d be pretty stumped. But let’s work it

out algebraically. 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. 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 multiplication sign gets confused

with the variable x, so they thought of either using

a dot if you’re multiplying two constants, or just writing

it next to a variable to imply you’re

multiplying a variable. 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. 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. 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. 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. Wherever we saw x, we’ll

now put our answer. So it’s minus 40/39, and

our original equation said that equals 10/13. Well, and once

again, when I just write the 3/4 right next to

the parentheses like that, that’s just another

way of writing times. So minus 3 times minus

40, it is minus 100– Actually, we could do

something a little bit simpler. This 4 becomes a 1

and this becomes a 10. If you remember when you’re

multiplying fractions, you can simplify it like that. So it actually becomes

minus– actually, plus 30, because we have a minus times

a minus and 3 times 10, over, the 4 is now 1, so all

we have left is 39. And 30/39, if we divide the

top and the bottom by 3, we get 10 over 13, which

is the same thing as what the equation said

we would get, so we know that we’ve got

the right answer. Let’s do one more problem. Minus 5/6x is equal to 7/8. And if you want to

try this problem yourself, now’s a

good time to pause, and I’m going to start

doing the problem right now. So same thing. What’s the reciprocal

of minus 5/6? Well, it’s minus 6/5. We multiply that. 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. We’re just left with x. 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. And assuming I haven’t

made any careless mistakes, that should be right. Actually, let’s just

check that real quick. Minus 5/6 times minus 21/20. Well, that equals

5, make that into 1. Turn this into a 4. Make this into a 2. Make this into a 7. Negative times

negative is positive. So you have 7. 2 times 4 is 8. And that’s what we

said we would get. So we got it right. I think you’re

ready at this point to try some level one equations. Have fun.

multiplication sign

The comment section reminds me why only 33.4% of Americans have a 4-year college degree.

if the x was an n or any variable letter, would it be the same thing? My teacher said yes but what about in algebraic equations?

U u suck👎👎👎

I'm watching this 13 years after this was posted, anyone else?

How many times did my brain go “but why?”

K, how do you convert negative improper fractions in to negative proper fractions?

And why do they “cancel out” and can you clarify exactly what that means?

I am confusion

Won

You are doing the lord's work man. Can't put into words how thankful I am for this.

Can’t be the only one who’s here the night before an exam and want to make sure that they know everything 😂😐

Im bad at school

Maths is used in everyday life

it’s 12:37 A.M., my math finals are tomorrow, and my teacher can’t teach for her life

pls pray that i pass i already have a low C

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