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MIT grad explains solving inequalities. This video focuses on solving linear inequalities. It shows when to switch the sign of the inequality, if you divide or multiply by a negative number, and is an introduction to how to solve inequalities in algebra. To skip ahead: 1) For a basic example of SOLVING AN INEQUALITY, skip to time 00:34. 2) For when you have to FLIP THE INEQUALITY SIGN when DIVIDING BY A NEGATIVE number, skip to 1:26. 3) For when you need to reverse the inequality symbol because you're MULTIPLYING BY A NEGATIVE number, skip to 2:42. The problems here are multi-step inequalities, or two-step inequalities. Nancy formerly of MathBFF explains the steps.
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Twitter: https://twitter.com/nancypi
Algebraic equations and inequalities: what is inequality math? What does inequality mean? An inequality is a number sentence that uses an inequality symbol instead of an equality symbol (=), which means it has a greater than sign, less than sign, greater than or equal to sign, or less than or equal to sign, instead of the normal equal sign in an equation. One linear inequality definition is: an inequality that involves a linear algebraic expression and inequality signs.
How to find the solution of an inequality algebra problem:
1) A simple, BASIC LINEAR INEQUALITY example you might see on a solving inequalities worksheet or problem set is the expression 2x + 3 [less than or equal to] 11. You can solve for x just like you would for an equality, or normal equation, by trying to get x alone. This is an example of two-step inequalities, or multi-step inequalities. The first step is to subtract the constant 3 from both sides, in order to move it to the right hand side, so that you have 2x [less than or equal to] 8. The second step is to get x alone on the left side by dividing both sides by 2 so that your answer for the inequality is x [less than or equal to] 4. In this case, solving the inequality used the exact same steps you would use to solve an "equal sign" equation.
Sometimes the steps are different from solving normal math equations. Solving for x is the same as solving a linear equality (-2x + 3 = 11) except that if you ever have to divide by a negative number or multiply by a negative number while solving for x, you must flip the sign, or switch the direction of your inequality symbol less than becomes greater than, for example). Here are the two cases of inequality problems WHEN YOU NEED TO REVERSE THE SIGN of the inequality because you're multiplying or dividing both sides of the inequality by a negative number:
2) DIVIDING EXAMPLE: For an inequality like -2x + 3 [less than or equal to] 11, after moving the constant 3 to the right side, you will need to divide both sides by negative 2 in order to get x alone on the left side for the solution. WHEN YOU DIVIDE BY A NEGATIVE NUMBER, you need to reverse the direction of the inequality symbol in your expression. In this example, after you divide out -2, you get x [greater than or equal to] -4 (instead of x less than or equal to -4) for the final solution. This example was also a two-step inequality problem.
3) MULTIPLYING EXAMPLE: For examples like (-1/2)x + 4 [greater than] 7, when you've moved the constant to the right side and have the inequality (-1/2)x [greater than] 3, the fastest way to get x alone is to clear the fraction by multiplying both sides by -2. This will cancel the 2 in the denominator and remove the negative sign in front of x on the left side. But WHEN YOU MULTIPLY BY A NEGATIVE, you have to flip the direction of the inequality symbol so that your answer is x [less than] -6 instead of x [greater than] -6. This problem was also a multi-step inequality.
Note on inequality rules: you don't have to switch the symbol if you're adding a negative number or subtracting a negative number: switching the inequality sign is only for when you're multiplying or dividing by a negative number.
For quadratic inequalities examples, compound inequalities, inequality math, inequality algebra, inequality equations, inequality symbols, inequality notation, and more algebra solver, equation solver, and inequality calculator practice problems that come up on worksheets, as well as more algebra, algebra 2, and college algebra mathematics videos, check out: http://nancypi.com
Yay first
plz upload the polynomial inequalities if you have it
Very good technique
hot stuff Miss Pi
Thank you Nancy!
omg hey Nancy we need Nancy merch
Yo!
just wanna say thanks for being the best math channel on youtube! love ya nancy!
Well I don’t love nancy
Perfect timing! I just learned inequalities this week! Thank you so much for the extra lesson. π
Thanks I always need to review these
Dangit I needed this for my test today lol. Well good video anyhow thanks!
Linear programming problem?
Extremely thankful for all of your videos, Nancy ππΌ
Hi @nancy,
Thanks for your help and efforts.
Can u please starts DEβS problems
more calc 2 please π
best math teacher there is , your follower from saudi arabia
and from IRAQ too.
Your friend from saudi arabia also
Damn Hagrid, didnβt know you started uni
Wheres my dragon
We waiting π₯ππ
Please do more videos. Love from India
I thought solution sets of inequality are expressed using set-builder notation and interval notation at the end of the answer? Is she missing something?
Hi nancy can u do a Rational Functions episode
Is any body watching maths? …or I am the only person.
I am watching… what’s wrong ?
This video will do nothing to help black people in modern day America. Thanks Obama!
Course for a level?
Hi Nancy. Thanks for the fantastic tuition videos. I left highschool without finishing to pursue a trade. Now I am in college doing a BEng as a mature student. Your videos have helped me out a lot over the past two years. Thank you.
Do you plan on doing a video on first order ODE?
I remember this in an online class. Your video explained this very well. Thank you
Can you please make a vedio on probability of indipendent events .
Good audio. The one before had too much echo.
Nancy is my president
My professor has a hard Russian accent and I can’t understand anything, your videos are clutch af!
Thanks you so much.
NANCY PLEASE DO VECTORS PLEASEEE!! I AM BEGGING YOU! YOU ARE THE BEST MATH TEACHER EVER! LOTS OF LOVE XOX
I love you will you marry me?
Notice me senpaiπ
fuck my math teacher i found a new one and she is hot
You are a total teaching legend.
Nancy i love the way you teach and especially your logarithm videos helped me a lot .Thanksπ
You are the truth! I am in math and it is so hard. You give me the strength to keep going. On my way back to class and when I get back I will do my homework with watching you. Thank you. Have a great day
man i hated math until i saw u Nancy , u are looking hot
Wierdo
Oooooof
How old are u
@Jayden Ng im 13
I so wish you were my math teacher. Please keep making videos you are so easy to understand and you speak clearly and deliver the message very patiently.
This video really helped because I have an exam next week, Thank you so much
Very well explained, like always! Keep it up!
thanks for helping us
2:24…….f the sign ??????ummmmm
Omg weβve been on this lesson for 2 weeks and this video literally taught me
Well, Now I’m not scared of mathematics. Thank you πππ»
Solving inequality in Math is way easier than solving it in the Society. Thanks Nancy
Fantastic video again from Nancy but for anyone wondering: Here is why it is flipped.
Imagine a number line. On the positive side lets say, “56 is greater than 23” (56>23). Then if we multiply both sides by -1, we essentially just change the side of zero they are on. They are still 56 and 23 away from zero, but they’re on the negative side of the number line now. (-56<-23<0<23<56) Essentially, a number larger than another number when positive, is smaller than the other number when they're both negative. Seems basic now I look at it, but didn't grasp it in the video.
Sen484 Awesome! Thanks!
that explained it thank you^^
Thanks
Wow omg thx for summarizing! I needed this since i really struggled to understand it thx!
OMG, she explained so simply.. I was always confused how and when did the sign changed? But you made me all clear..THANKYOU
Nice, I make similar videos. I know, nobody asked π
Yh she really did
Franck’s Notes hahaha your SO funny! π
This was extremely helpful but I can’t find the compound inequality video you referred to.
thankx mam
Luv u from Pakistan Nancy !
As a sociology major, I grossly misread the title.
I did learn that mathematical inequalities are much easier to solve compared to social inequality, so thanks!
Sorry, my dude, this is a math video, not a Cultural Marxism video. For that you’ll have to see Crash Course Sociology. If you don’t have time, let me summarize: muh white man bad, women good, gays better. There you have it in a nutshell.
@The Goodly Dragon ok but nobody asked
@The Goodly Dragon Thank youuuuu i got a A* how did you even know that?????
The Goodly Dragon who are you
@The Goodly Dragon I do not mean to sound like an egotistic and presumptuous jerk but given that I graduated with honours with a BA in Sociology, I would have to say that it appears that you know little about the complexities of sociological theories. However, I apologize if my presumption is incorrect.
On a side-note, given the chaos currently occurring throughout the U.S., I would recommend taking a quick look at Das Kapital (1867) by Karl Marx, and The Permanent Revolution (1930) by Leon Trotsky.
Where r u from
Hi Nancy, great job! Please show each step for new comers. π
Thanks 4 clearing my concept
Hi, I had a question in regards to solving this inequality:
x+1/2x-3 < 1/x-3 Iβm not too sure how to solve it since we donβt know if x is positive or negative so you have to multiply the denominator by x^2
How to Do Stuff with Ethan we donβt know if x is – or + it is an unknown
@Marie Hill true. never mind.
How to Do Stuff with Ethan thank you anyways! Hope youβre doing good
@Marie Hill sorry i could not help you…
This is how I did it:
(x+1)/(2x+3) < 1/(x-3) If x-3 > 0, x > 3:
(x+1)(x-3)/(2x+3) < 1 2x+3 must be positive because x > 3
(x+1)(x-3) < (2x+3) x^2 - 4 x - 6 < 0 If x-3 < 0, x < 3: (x+1)(x-3)/(2x+3) > 1 (flip the sign because x-3 is negative)
If 2x+3 < 0, 2x < -3, x < -3/2. (x+1)(x-3) < (2x+3) (flip the sign again if x 2x+3 is negative) x^2 - 4 x - 6 < 0 If 2x+3 > 0, 2x > -3, x>-3/2:
(x+1)(x-3) > (2x+3)
x^2 – 4 x – 6 < 0 So: If x > 3 then x^2 – 4 x – 6 < 0 If x < -3/2 then x^2 - 4 x - 6 < 0 If -3/2 < x < 3 then x^2 - 4x - 6 > 0
Solve the inequalities:
x^2 – 4x – 6 < 0 Complete the square: (x-2)^2 β‘ x^2 - 4x + 4 (x-2)^2 - 10 < 0 (x-2)^2 < 10 x-2 < sqrt(10) or 2-x < sqrt(10) (because 2-x and x-2 give the same squared) x-2 < sqrt(10) x < sqrt(10) + 2 or 2-x < sqrt(10) -x < sqrt(10)-2 x > 2-sqrt(10)
So:
2-sqrt(10) < x < sqrt(10) + 2 This is only true when x > 3 or x < -3/2 so If x > 3:
2-sqrt(10) < 3 so it cannot be a solution when x > 3.
So one solution is: 3 < x < sqrt(10)+2 If x < -3/2 then sqrt(10) + 2 cannot be a solution because it is more than -3/2. So another solution is: -3/2 < x < 2-sqrt(10) The solutions for x^2 - 4x - 6 > 0 are:
(x-2)^2 – 10 > 0
(x-2)^2 > 10
x-2 > sqrt(10) or
2-x > sqrt(10)
x > sqrt(10) + 2 or
-x > sqrt(10)-2
x < 2-sqrt(10) So the solutions to x^2 - 4x - 6 > 0 are:
x < 2-sqrt(10) x > sqrt(10) + 2
x^2 – 4x – 6 is only true when -3/2 < x < 3 -3/2 < 2-sqrt(10) sqrt(10) + 2 > 3
Since both have to be true, there are no values for x that satisfy the inequality when -3/2 < x < 3. So the only solutions to the original inequality (x+1)/(2x+3) < 1/(x-3) are: 3 < x < sqrt(10)+2 or -3/2 < x < 2-sqrt(10) Actually you might have meant x+(1/2x)+3 < (1/x)-3.
She reminds me of the daughter in the Incredibles.
oh yeah… She kind of does lol
dude not now
the daughter in the Incredibles is Violet
omg yes
tanx nancy
Hotter then chicken
I should have watched this before my test π
Rip π΅
Did u pass ur grade
At least now you know where to go in the future
What a rare sight to see these days, an attractive girl who is also intelligent
You must live under a rock lol
2:24 fu*k the sign……… π
She said flip
Could you stop cuzzing!
Thank you so much Nancy! I’m at grade 7 and we’re learning this lol who else???
Grade 9
I’m in 9th grade and I’m learning this lol ^^
Grade 6
@Debora Tintisan me too
year nine :/
R u from india nancy….Nice math teacher
Gaanduβ€οΈ bht acha parhati hyπ
Gaandi bol Bhai π€£
This video is super helpful thanks!
-6
asjad abrar easy
thanks …it helped me alot
Merci
Thank you so much
Thank you this is the basis for Linear Programming in my Grade XII.PLEASE DO VIDEO ON ALL TOPICS WHICH ARE BASICS FOR
CALCULUS,
VECTORS,
INVERSE TRIG,
MATRICES,
DETERMINANTS these topics
i was scared that my parents may come from back while watching your vedio because they wouold think that i must be watching any models content
I don’t understand why the fraction -1/2 needed to be multiplied by -2. If the fraction was -1/4 would you multiply it by -4 etc?
LolDarrellLol Because its the -1/2 the respricol is -2/1 which = -2
And yes
Thanks for making this video
Beautiful and wise ….. Best explained.
Can u like… Be my teacher
Such a soothing teacher.
SO TRUUUEEE!!!!!!!!!!
I was wondering if anybody said that in the comments
S C H O L A R
I mean this is extremely rudimentary, wish you went in depth with quadratic inequalities
YE I KNOOW…..
Anyone else not focusing on the vid
Im a bit confused. When you canceled out the 2 in the denominator, does that mean that the 1 from the fraction is a whole number or is that still part of a fraction. 2nd question is that, why do we always have to multiply by -2?
Please do a video on quadratic inequalities
May i go to the restroom?
We love a math queen
I really liked the idea of ur teaching ππππππππππ
have a trouble with (x+3)square>(2x+3) which one is a b and c thanx in advance
This is how I would solve it:
(x-3)^2 > 2x+3
Expand:
(x-3)^2 β‘ (x-3)(x-3) β‘ x^2-6x+9
x^2 – 6x + 9 > 2x+3
Move all terms to one side:
x^2 – 8x + 6 > 0
Complete the square:
(x-4)^2 β‘ x^2 – 8x + 16
(x-4)^2 – 10 β‘ x^2 – 8x + 6
(x-4)^2 -10 > 0
Isolate the square:
(x-4)^2 > 10
Square root both sides:
x-4 > sqrt(10)
x > sqrt(10)+4
since (x-4)^2 β‘ (4-x)^2, another solution is 4-x > sqrt(10)
4-x > sqrt(10)
-x > sqrt(10)-4
Divide both sides by -1, and flip the signs.
x < 4-sqrt(10) So the final solutions are: x > sqrt(10)+4
x < 4-sqrt(10)
Holy thanks for the advice and help tks so much I have a big test coming with me lu k
I love u
Can you help me with this problem 3+9Γ>4(Γ+7) thanks
3+9x > 4(x+7)
3+9x > 4x+28
9x-4x > 28-3
5x > 25
x > 5
So you subtract three for every question
How to solve : 5(β5)^x+5 = (β5)^2x+7
So,
X=?
Is she writing backwards so we could see it normally
yep
Still confuzed but less
GUYS YOU DO REALISE THAT SHE IS WRITING BACKWARDS ON A MIRROR
DUDE THATS HARD!
Common misconception about this channel, she writes behind a glass board and the camera is on the other side of the glass board, then the video is reversed/mirrored
If she is a soothing teacher like to my comment
Gracias amiga
You are the best!
1:16 you got it wrong
No, it was correct she simplified it.
Mxxnlightx UwU yes it is she divided it therefore changes the way it points
The way she writes 11 is weird, but I guess I shouldn’t criticize since she’s able to write backwards.
;0
boooooooo
booo
this really help me in math on my homework thank you so much
0:30 π€£π€£ππ “If you don’t know what am talking about this is the right video for you”! BARS!
I love it, she just made it easy for me.
thank you Ms.Nancy its help me a lot, iam taking the FE exam on april 2020…
how was that exam lol
Josh s been cancelled
Lol
thank you thank youuu
Hold up… this person is writing backwards while explaining math
What is this level of brainpower
Daniel Kim Uh…
Maybe she used reverse filter?
#NamcyPi You are the most beautiful teacher I’ve ever had. Thank you
Your method of teaching is so simple and interesting. Thanks a lot from Punjab, India.
No nigga!!
You mentioned that you have videos for Quadratic inequalities on your channel, but I could not find them. Is that something you would consider covering?
lol i was watching this video and my mom tried to start teaching me it backwards (aka the wrong way) this video teaches better than my mom
idrk what grade level this is at but im still confused
Josh s Iβm in grade 6 and weβre taking this
Please tell me Iβm not the only one who still donβt get it!!
Can we also divide negative half by another negative half
I was a little surprised that a justification for reversing the inequality after multiplication by a negative was not given. I always found that that extra insight often helped me remember.
Even though you are a math teacher
You are hot
Hello Nancy, nice choice of content. I also have created a channel with the same content. I am Teacher Marz and I am very happy to subscribe in your channel to collaborate…
Tq
good nancy β€β€
You are beautiful π
Thank you Nancy!! Well explained
Thanks a lot
Hey Nancy, great video I am glad I found you here on YouTube and subscribed. I really love your style and how you present the material, very calm and clear, I need to learn how to control my breathing in my videos π I make similar content.
I watched like 15 different inequality videos before this one and just heard “blah blah combine like terms blah blah subtract blah blah divide blah blah greater than or equal to blah”. And this 5 minute video actually made sense.
I’m telling yah, hot teacher with a nice voice makes everything easier to learn.
Certainly doesn’t hurt. If I had more hot teachers in school, maybe I wouldn’t be where I am now!
can u be my math teacher!!!!!!!
Thank you you helped me so much
Yes nancy. I hate maths but nancy makes it better
This helped thank uuuu
Wow amazing
Love it
I paid more attention to her than my math teacher.
But in serious, thanks for the step by step explanation!
I don’t understand
Really great and calm teaching method.πππ
Is this a mirror
How is she so good writing numbers backwards
Thanks a million!!
You didn’t say where the -2 came from at 3:17 to multiply against the fraction. Is it from the bottom part of that fraction?
thank yo mem
Gurl thank u so much, this helped me alot, π
it sounds like she is bored from doing math
Thank you
Simple and clear explanation
Thank you sooo much π₯°β€οΈππ»ππ»π―π
Thank you Madam