Welcome to the presentation

on solving inequalities, or I guess you call them

algebra inequalities. So let’s get started. If I were to tell you that,

well, let’s just say x is greater than 5, right? So x could be 5.01, it could be

5.5, it could be a million. It just can’t be 4, or 3, or 0,

or negative 8, and actually, just for convenience,

let’s actually draw that on the number line. That’s the number line. And if this is 5, x can’t be

equal to 5, so we draw a big circle here, and then we would

color in all the values that x could be. So x could be just the small–

it could be 5.0000001. It just has to be a little bit

bigger than 5, and any of those would satisfy it, right? So let’s just write some

numbers that satisfy. 6 would satisfy it, 10

would satisfy it, 100 would satisfy it. Now, if I were to multiply, or

I guess divide, both sides of this, I guess we could say,

equation or this inequality by negative 1, I want to

understand what happens. So what’s the relation between

negative x and negative 5? When I say what’s the relation,

is it greater than or is it less than negative 5? Well, 6 is a value

that works for x. So negative 6, is that greater

than or less than negative 5? Well, negative 6 is less

than negative 5, right? So let me draw the

number line here. If we have negative 5 here, and

let’s just draw a circle around it because we know it’s not

going to be equal to negative 5 because we’re deciding between

greater than or less than. So we’re saying 6 works for x. So negative 6 is here, right? So negative 6 is less than

negative 5, so is negative 10, so is negative 100, so is

negative a million, right? So it turns out that negative

x is less than negative 5. And this is really all you have

to remember when you are working with inequalities

in algebra. Inequalities, you can treat

them just the way– a greater than or less than sign, you

could treat them exactly the way you would treat

an equal sign. The only difference is, if you

multiply or divide both sides of the equation by a negative

number, you swap it. That’s all you

have to remember. Let’s do some problems,

and hopefully, that’ll hit the point home. And if you ever forget, you

just have to try– you just remember this: if x is greater

than 5, well, then negative x is less than negative 5. And keep trying out numbers. That’s what’s going to give

you the best intuition. Let’s do some problems. So if I said that 3x plus 2 is,

let’s say, less than or equal to 1– well, this is a pretty

easy equation to solve. We just say 3x– let’s subtract

2 from both sides, and when you add or subtract, you don’t do

anything to the inequality. So if you subtract 2 from both

sides, you get 3x is less than or equal to negative 1, right? And then, now we’re going

to divide both sides by 3. We get x is less than or equal

to negative 1/3, right? And notice, we didn’t

change anything because we divided both sides

by a positive 3, right? We could have actually

done this equation in a slightly different way. What if we subtracted

1 from both sides? So this is another

way of solving it. What if we said 3x plus 1 is

less than or equal to 0, right? I just subtracted 1 from both

sides, and now let’s subtract 3x from both sides. And we get 1 is less than or

equal to minus 3x, right? I subtracted 3x from here, so I

have to subtract 3x from here. Now, I would have to

divide both sides by a negative number, right? Because I’m going to divide

both sides by negative 3. So I get negative 1/3 on this

side, and based on what we had just learned, since we’re

dividing by a negative number, we want to swap the

inequality, right? It was less than or equal,

now it’s going to be greater than or equal to x. Now, did we get the same

answer when we did it both– two different ways? Here, we got x is less than or

equal to negative 1/3, and here we got negative 1/3 is

greater than or equal to x. Well, that’s the same answer,

right? x is less than or equal to negative 1/3. And that’s– I always

find that to be the cool thing about algebra. You can tackle the problem in a

bunch of different ways, and you should always get to the

right answer as long as you, I guess, do it right. Let’s do a couple

more problems. Oh, let’s erase this thing. There you go. I’ll do a slightly harder one. Let’s say negative 8x plus 7

is greater than 5x plus 2. Let’s subtract 5x

from both sides. Negative 13x plus 7

is greater than 2. Now, we could subtract

7 from both sides. Negative 13x is

greater than minus 5. Now, we’re going to divide

both sides of this equation by negative 13. Well, very easy. It’s just x, and on this

side, negative 5 divided by negative 13 is 5/13, right? The negatives cancel out. And since we divided by a

negative, we switch the sign. x is less than 5/13. And once again, just like the

beginning, if you don’t believe me, try out some numbers. And I remember when I first

learned this, I didn’t believe the teacher, so I did try out

numbers, and that’s how I got convinced that it

actually works. When you multiply or divide

both sides of this equation by a negative sign, you

swap the inequality. And remember, that’s only when

you multiply or divide, not when you add or subtract. I think that should give

you a good idea of how to do these problems. There’s really not

much new here. You do an inequality– or I

guess you could call this an inequality equation– you do it

exactly the same way you do a normal linear equation, the

only difference being is if you multiply or you divide both

sides of the equation by a negative number, then you

swap the inequality. I think you’re ready now to

try some practice problems. Have fun.

anyone else in 8th grade?

What app are you using to write?

I was 2 years old when this video came out. Also you suck middle school honors classes.

i hope this helps to ease my struggle in algebra1 class

I got little bit confused on the negative

so bleary

I just wanted to watch Roblox videos

This music is great!

I don't use the method of subtracting because I wasn't taught that one (although I understand it from videos) but if I were to just change the things like:

3x = 1

Well, then I'll move the 3 to the other side and I get

X= 1/3

How does the multiplícate/divide negatives rule apply to this? (I feel like this is a dumb question )

confused!

0:44

For this inequality is it able to takeaway 2 first or the x is supposed to be done first?

I dont like how he doesnt explain…he kinda just tells you what to write and that is why i dont get this stuff

MY 7th GRADE TEACHER IS A GENIUS

Is anyone else using this for Khan Academy?

Sure, this totally makes sense.

I suck at math

2017

Khan you are the best teacher in explaining math.

can you please do a video on how to do inequality such as h minus sixteen is less than twenty-four?

Why and how did you change -5/-13 to 5/13

Thanks help a lot 👍

why do we need to learn this in school?

Thanks this makes sense how are people confused

so lost

Hello. I just wanna ask how do you solve it when x^2-5x+1<0?

Please help me how to solve this? 🙁

thank you!!

How do I know if I should use addition, subtraction, division etc. to solve the equation

6:15 Negative numbers

Some of this is confusing

I was confused but this helped me so much! thank you.

2018?

To make live WAY more simpler DO NOT have your variable in a negative form. Always solve so the variable is positive and then disregard the flipping of the inequality sign. That's just a pet peeve of mine.

v. important concept in algebra

no clue

#betterthanmymathteacher

This REALLY helps with my math homework!!! Thanks!!! =)

Nice explaination!!

For anybody who is confused basically when you divide both sides by a negative number, you swap the inequality

WOW KHANACADEMY YOU 10

look at this dude i dont understand your inequalties math some people know how to do it better than you punk

Good sir but u explain in bit confusing way

I can't I just want to die

Watching this video night before the staar test (major exam in Texas)

5:32

i dont understand… why did the sign switched to less than?????

video starts at 0:00

Lost after he drew the number line😂

I get it

thank you so much

I learn't this in 6th grade and forgot you are a live safer phew thx

These comments though!

Uhm I'm confused a little bit, why do the final answer became less than?

LOVE IT

this was confusing till I replayed it and he made way to easy thx bro even more 10 years later and helps people

I'm honestly so happy I found this. My teacher taught it in like 10 minutes for one day and I have a test on it tomorrow and it makes way more sense now

Thank you! helped alot

Currently have 5 minutes until school for a test, I definitely going to fail it. -_-

Could u do more examples plz thx

I love you so much 😭😭😭

long live to Khan academy

How did you become so genius

Excellent content. I do see that you should change to a better quality software such as that of similar YouTubers

I didn't get a thing he said. anyone else?

thank you so much i cant with math this really helped

OMG I FiNaLLY KNOW HOW TO DO INEQUALITIES!!! Thanks khan academy!! You are now my homeschool tutor

OMG SO HELPFUL!!!!!! I HAVE A TEST OVER THIS TOMMOROW!!!!! THANK U!!!

Wow everyone has there school accounts here lol

This is confused. 🙂

Good he’s my good online math tutor

you are the bob ross of educational videos

I will report this tomorrow in my class 😭😭

So, a greater than or less than sign is essentially the same as an equal sign? But why?

Even though I haven’t ever heard of this topic I still understood at the end!

what am i supposed to do in the 3 min. part of the vid I get nothing help?

Still confused

Good, but I can't read it!

ummmm so at 5:14 why is the 5 negative? I keep looking to see why, but I still have no clue. I'm confused.

So confused

Why do 6th graders need this ;-;

'19 anyone?

2019 anyone

I like these videos.

Thanks Khan, you reminded me what the rules were for a project

The problem at 5:00 how do I know which side I subtract from

I understood all of it (⌐□ل͜□)

Umm after the first example complete confused.

Man this is so confusing these comments are killing ma😂😂😂

12 years ago

Learnt until 4:03 then complete confusion

Enequality is my enemy

Khan is Legend.

with -8x + 7 > 5x + 2

you said to minus 5x from both sides, why not 8x. please help

Exactly what I needed

I don't understand the last part

Got so confused cause I thought that the greater than sign was a 7

Marksman?

This would be helpful if i wasnt extremely dense

What

this video is older than me :/

Helped me a lot