Let’s Solve This Equation…Step-By-Step…

[@frankprospector115]

I hated algebra and geometry in school. but now that you are explaining it I am really enjoying it. Glad I found this channel.

[@johnquestel4852]

Love it! I'm 66 and haven't done algebra since 7th grade... it's still fun... but jeeze have i forgotten alot...

[@BobBob-uv9fq]

Yes ,like this format ,not assuming folk know stuff ,but too much chat at the start

[@celiagorleski2716]

Almost 68 and I can still do it!

[@bobwineland9936]

Hurray!!! I'm 76 and relearning all this stuff. Good luck with math.

[@jeromekovacik1198]

Hi John, In one case you added a -1/2 to cancel the 1/2. But in the case of 7/2 you multiplied by the reciprocal. You could have added a 7/2 to each side to keep things the same during the problem. However I guess you could do the multiplication regarding the 1/2 as well. Same answer... Enjoying this at 62

[@hughsonj]

Instead of dealing with a fraction, I multiplied both sides by 2 and still came up with the correct answer.

[@cbesthelper404]

Yes, that is how I did it too. It clears the denominators, making the equation so much easier to solve.

[@philliphonsbein7481]

Sir ! You are brilliant!

[@NerdWithLaptop]

-3(x-1) = x/2 + 6 -3x + 3 = x/2 + 6 On the left side, add 3 and subtract 3. -3x + 3 + 3 - 3 = x/2+6 3 + 3 = 6 -3x + 6-3 = x/2 + 6 -3x - 3 = x/2 To get from -3x to x/2, we need to add 7x/2. -3 = 7x/2 Multiply both sides by 2/7 -6/7 = x SECOND STRATEGY: -3(x-1) = x/2 + 6 -3x + 3 = x/2 + 6 -3x + 3 - x/2 - 6 = 0 Rearrange the terms -3x - x/2 + 3 - 6 = 0 -7x/2 - 3 = 0 For any linear equation ax + b = 0, ax + b - b = 0 - b ax = -b x = -b/a -7x/2 - 3 = 0 (-7/2)x - 3 = 0 x = -(-3)/(-7/2) x = 3/(-7/2) Bring the 2 and the negative sign up to the top x = -6/7

[@CIE504]

Question: I thought when adding a whole number to a fraction, you are supposed to put it over one and get a common denominator?

[@MrMousley]

Let's work through this one step by step .. - 3 (x - 1) = 1/2x + 6 do the brackets/multiply bit first - 3x + 3 = 1/2x + 6 and now multiply everything by 2 to get rid of the fraction - 6x + 6 = x + 12 add 6x to both sides 6 = 7x + 12 and now subtract 12 from both sides - 6 = 7x and now divide both sides by 7 - 6/7 = x

[@fadelali330]

Thanks.

[@tomtke7351]

To achieve ?? an end equation where X is on left side and a number is on the right side. So sum up X's and sum up numbers.

[@markjakeway2035]

Is there some 'rule' in the US that the variables have to be on the LHS? Why? it's just making the equation solving process harder by having to deal with negative numbers in addition/subtraction which is more prone to errors. Second time I've seem this in one of your videos so I assume it is a rule?

[@Afrocanuk]

I was thinking the same thing. I don't see why it should matter.

[@danielcase1046]

I does matter, each every expression

[@cbesthelper404]

@@danielcase1046 In the final answer, it doesn't matter. x = 2 is the same as 2 = x.

[@danielcase1046]

This dude is right on all the🤩 time

[@wristdisabledwriter2893]

You didn’t do my favorite step that I usually do first. I multiply both sides by 2 to get rid of the fractions in this question.

[@quinnhogue3252]

Do I do distributive property first or multiply the -3 and 2 first

[@wristdisabledwriter2893]

@@quinnhogue3252 you can do either first but I found it faster to multiply by 2 first

[@ratneswartamuli4215]

We know d simple method than yours

[@Herlongian]

Just put parenthesis around the whole equation and multiply by 2. That takes care of both sides in one move.

[@thomassicard3733]

I get a SMILEY FACE!!!! WEEEEE!!! I'm old, but I ain't done yet!!! 🙂 Love your teaching style, sir.

[@stanwebb3480]

-7/2X= 3/1..... my choice is means equals the extremes and got your answer...... -2 times 3 =-6 next step -7X times 1+=-7X.... -7x =-6 divide both by -7 and get x=-6/7

[@mendozajovy]

Isolate x from the numerical values is the general principle for solving x

[@muradmuhammed9441]

THANKS a lot

[@achrace.profrichardachara]

But what happened to bodmas (or pemdas)? Why did you ignore the brackets (or parentheses) at the start of the solution? Okay, I get it now. You implicitly treated (x - 1) as irreducible and then proceeded to the 2nd stage of multiplying each of those 2 individual terms within the brackets by negative 3.

[@ginoliessens3024]

Such a simple equation! I could solve it in my head in less than 30 seconds and this video is 13 minutes long!

[@richardlapinski8303]

You are a special person Gino.

[@thomassicard3733]

My unadulterated reverence in worship of your cerebral magnificence, Mssr. Liessens. I am in utter awe and humbly bow in servitude to your excellence.

[@cbesthelper404]

Of course the video is longer than the time to solve it in your head. The instructor has to explain each step. You didn't.

[@Notintimidated2013]

That is “fun” to me. Not so much to rest of the world.😁👍🏻

[@ratneswartamuli4215]

U make d system complicated !!

[@aryusure1943]

BY way of reviewing what I learned here in the pass 6 monthsor so I can say that I got the right answer even if I shuffled my variables a little bit differently than you. It worked and I did not forget to start with the distributing part of the problem. :) I even plugged in my solution at the end to make sure I got the right answer. I should get an additonal star for being such a good student. ;) Just kidding! :)

[@Kerbeygrip]

I am 77 and got 0.86. Also correct!

[@fredgs2]

My old brain figured this one out in two minutes!

[@innocentodenigbo7284]

That's good.

[@FOTWC]

9:02 if you subtracted 1 over 2 why did you add -3 and -1 over 2? why didn't you subtract ?

[@uwdock2116]

Because adding a negative term is the same as subtracting a positive term. He added a negative term on the left and subtracted a positive term on the right. Think of it this way if it helps, he added -1/2 X to both sides - the two negative term on the left are added but the negative and positive terms add to 0 on the right.

[@ratneswartamuli4215]

We donot understand why addition n substraction are necessary ?we have d simple method.

[@DLadybeeTV]

Acsually I am still helpful but thanks😊😊😊😊😊😊😊😊😊😊😊

[@cpretty23]

Love your videos, the introductions are too long. I get it take notes‼️

[@Kleermaker1000]

This was an easy one. Better give the right answer before the explanation starts. :)

[@messiahjonz]

13:03 video that could/should have been 3:00 maximum.

[@erniehogan2404]

81 in Scotland and nae borra!

[@orobleh77]

Answer: 3/-3.5

[@mariareale9040]

Remembered too.

[@蘇大軍-n7x]

I’ll x2 in the first, it’s easier

[@quinnhogue3252]

How do you do that

[@Arcadia61]

@@quinnhogue3252 Multiply each term by 2 at the beginning to get rid of dealing with fractions. If you multiply throughout by 2 you get: -6(x-1)=x+12. Then open up the brackets to get -6x + 6=x+12. Rearranging the equation, we get -6x-x=12-6. Collecting like terms, -7x=6. Dividing both sides by -7, we get x=-6/7.

[@rickjohnson4544]

Enjoyed that. Took me back more than 40 years ago. Still remember too 😀

[@totoitekelcha7628]

-3x -1/2x Shouln't the answer be 2 1/2x? Why you add it? If minus sign is change into plus sign than you should substraction it not addition. I gt confuse. 9:14

[@eigerview1]

Me too. I am still perplexed about the answer not being 2 1/2x. I thought you had to perform the same steps on both sides of the equation.

[@cbesthelper404]

A negative minus a positive is the same as a negative plus a negative. For example, -3 -2 equals -3 + -2 = -5. Whenever you subtract, you may rewrite it as adding the opposite (sign).

[@Herlongian]

My first step is to double the equation to turn 1/2x into x.

[@theophonchana5025]

#distributiveproperty #polynomial #binomial #linearequation

[@chetanjoshi2159]

-1/2, or - .5

[@Ceesmeezy]

I thought my 5th grade math was bad but the heck who added letters. Like our algebra is ez.

[@edwardflores4846]

Math is like a puzzle

[@chetanjoshi2159]

X equal to -6/ 7

[@futuretrunks9257]

10:37 Can someone explain to me, how did we get 1x? What happened there?

[@ginenice4185]

Because he multiplied both numerator and the denominator is 14/14 is equals to 1 and when you multiply a negative to negative number it will become positive

[@futuretrunks9257]

@@ginenice4185 Thank you! So every single time the numerator and denominator is the same we turn it to 1?

[@name3583]

@@futuretrunks9257 It's common sense. 1= 1/1 = 2/2 = 3/3, ..., 100/100, ..., but there is a exception. 0/0 = undefined.

[@kjc7344]

@@futuretrunks9257 when you multiply fractions you multiply the numerators together and the denominators together, if anytime you multiply a fraction by its reciprocal it will equal 1

[@cbesthelper404]

@@futuretrunks9257 It reduces to 1.

[@chetanjoshi2159]

Have u the answer

[@kjellg6532]

Multipy with 2 and clean up. Takes less than 1 min, not 13!

[@DF-cm5rz]

I feel if your correlate it to the real world kids will accept it a lot easier! I like to call the style you are using "Therapeutic Explanation "

[@CraigLMoran]

Dude, where were you when I was in school. Lol

[@mathbbn2676]

well

[@danielcase1046]

It is a war against + and -😁

[@fadelali330]

X=6/7

[@Brykk]

Im guessing you have a bit of a challenge with kids picking up your lessons the first time through? I can tell you that your approach has a major flaw. The psychology of keeping someone engaged in a lesson shows that if you are teaching in steps, like you are doing here, and you leave a step that isnt fully explained, the students mind will get stuck on that unexplained point and have trouble moving forward with the comprehension of the rest of the lesson. When you explained the situation with the positive and negative numbers on the first step and said that if you arent up to date with the rules for that step, just see another video later on how to take care of it. You just created a hurdle because they will be thinking about how to deal with that situation and they will tune out the rest of the lesson (at least to a degree) because they are busy thinking about how to solve the first part. Its just like when someone has trouble with comprehension in reading because they run across a word they dont know the definition for, the rest of the reading assignment will be compromised because their brain will keep reverting back to trying to figure out the meaning of that one word, and they wont be able to fully focus on what came after that one word.

[@ShirleyLarson-LaMarche]

I can see it in you and you can see it in me…..flaws. All right ….you do a couple of hundred classes

[@Brykk]

@@ShirleyLarson-LaMarche and there it is. Instead of just being butthurt, how about adopting what most educators criticize their students for………learn to accept constructive criticism. Im not bashing anyone here. I was trying to point out a flaw and creatively suggest how to fix the problem. Thats all.

[@cbesthelper404]

@@Brykk Actually, your criticism was not constructive. If a student is here without a mastery of integers, then it is incumbent upon the student to go back to study integers. A teacher cannot bring every single student in class up to speed. That is the student's responsibility and the reason for prerequisites.

[@williampapadopoulos8145]

x= -6/7

[@jimprovencio9102]

Reciprocal

[@danielcase1046]

the remains are always.🙂

[@jammercap02]

I got the speed of light

[@ቢቺኢትዮጵያ]

Some of it is tricky

[@vwnut13]

For the love of god multiply everything by 2 to get rid of the fraction.

[@danieldennis9831]

- 6/7 ? I really need to grab paper instead of doing it in my head. Lol

[@kjellg6532]

x= - 6/7, in my head in about 1 min. Why is he using 13 minutes?

[@ykmjc]

less talk, more of solving the problem pls pls pls

[@michaelsevali7659]

I don't like too much talking

[@deannapardue3162]

"prolem" instead of problem, "recipical" instead of reciprocal, okay, definitely not a word pronunciation lesson...

[@danielmadden9691]

-6/7

[@mayeerahbrits1372]

I tried... No good at it... 🙄

[@farmertice7064]

Well done but a bit wordy.

[@nikkitytom]

This would be a lot more "fun" if the explanation were simplified with far less blather. This could be explained in 3 minutes without rambling around. 13 minutes is not fun! I'm fossilized by the verbosity!

[@chetanjoshi2159]

Talking

[@tevman69]

LMAO! Not really 😩

[@henkhu100]

at 3:47. : this is a negative 1. Oh? The - sign is an operation: substract 1 from x. The - sign has nothing to do with a "negative1". Please teach the students no wrong things: there is a major difference between the -5 in -5 and 8-5. In the first expression it tells us that we have the number "negative 5", in the second expression it tells us to substract 5 from 8. Please stop teaching math in this way.

[@cbesthelper404]

The instructor is correct. The "1" is to be viewed as -1 when distributing. In your example, your second expression is the same as 8 + -5. Students need to know this.

[@henkhu100]

@@cbesthelper404 You are wrong @CBEST HELPER! In my example the expression 8-5 is not the same expression as your 8 + -5 The answers are the same but that does not mean that the expressions are the same. For instance 4*6 and 8*3 are different expressions, but the results are the same. In 8 -5 you calculate a difference, it is a substraction. In 8 + -5 you calculate a sum, you add up values. In 8-5 we have the values 8 and 5 and we substract them, in 8 + -5 we have the values 8 and -5 and we add them up, and as mentioned the result is the same but the expressions are different. Students need to know this, is my experience as a math professor for over more than 40 years (high school and university level). The instructor is wrong, as, by the way, in many of his videos.

[@cbesthelper404]

@@henkhu100 The expressions are the same. Subtraction is merely adding the opposite. If a student would like to throw away subtraction and only deal with addition for the rest of their lives, they are free to do so. Even the example that you used, albeit the two expressions display different numbers, are technically the same if you were to rewrite them in prime factorization form. What the instructor said in the video was correct. A minus sign in front of a positive value may be referred to as "negative...."

[@henkhu100]

@@cbesthelper404 What you don't understand is that the - symbol has two different meanings. It can mean the opposite of a number or it can stand for an operator, a substract operator. And in an expression like 8-5 we have the - sign as an operator. Because if in 8-5 it is a "negative value" sign then we have two values 8 and -5 but we have no indication what to do with them, there is no operator between the two values 8 and -5. That is why 8 + -5 is completely different: we have two values, again 8 and -5 but now we know what to do with them: add up. That we can change a substraction 8-5 into an add up operation 8 + -5. does not mean that there is a value -5 in the first expression. We introduce that value -5 in the second expression by changing the substraction into an add up operation. Your remark about the prime factorization is not relevant. 4*6 and 8*3 are two different expressions. Even 8*3 and 3*8 are different expressions., 8*3 is short for 3+3+3+3+3+3+3+3 and 3*8 is short for 8+8+8, like 3a is short for a+a+a) An expresision does not only result into a value it also has a symantic meaning. What you say in fact is that if we have the same result we have the same expressions. So sin(pi/6) is the same expression as 4/8. because both are equal to 0,5

[@cbesthelper404]

@@henkhu100 You sound confused, and I must say arrogant by assuming "what you don't understand". Laughable. I stand by my statements and maybe it is you who needs to realize. Consider the polynomial: x^2 - 5x + 4, the coefficient of the second term is negative, and I need not rewrite as addition to deem it so. By the way, I've been teaching math (and physics, chemistry, statistics) longer than you, so don't assume you are communicating with an inferior.

[@chetanjoshi2159]

Ok finish talking.

[@williamcastleberry7338]

Where in the devil would use this in real life. I spent over 40 years working construction. I would have been laugh off the jobs if I had come out with this kind of horse manure. There's no place for it in the real world.

[@VanillaLimeCoke]

It's basically another simple but more complex equation For instance in my job I look at about a week's worth of total figures. If I was to estimate what it would look like for a whole month I could use a simple equation. Let's take October 2021 for example.... 1 week or more exact 6 business days and I have a figure. I want to guesstimate what the month will look like. Well simple way is just to multiply my figure by 4 weeks and I have a good possible number. But let's get more possible. There are 21 business days. So let me take my figure and divide it by 6 then multiply that by 21....to get a better more realistic projection. Another such example would be I have figures for this year from 10 months, but January and February were not good for various reasons (if you live in the North...construction must not be too good in those months too, especially if it's outside). Let's total my figures then but then subtract January and February. Let's then divide that by 8 to get the monthly average (not counting those 2 bad months). Now barring the example I gave above if January and February worked well for me....this is basically the figures I should have had for each of those months. Hope this helped a little. Of course I can also use the little excel feature to just get the average of my numbers for those 8 out of 10 months just by simply highlighting them

[@PureExile]

Jesus Christ. Save yourself 13 minutes and read this: -3(x-1) = x/2 + 6 -6(x-1) = x+12 (multiply both sides by 2) -6x+6 = x+12 (remove the brackets) -6x+6-x = 12 (subtract x from both sides) -7x = 6 (subtract 6 from both sides) x = -6/7 (divide both sides by -7) #

[@cbesthelper404]

The only thing is if he were to work it that way, he'd lose 99% of the audience.

[@PureExile]

@@cbesthelper404 Hey, maybe. I used to be extremely critical of this guy but he might be catering to a niche market of which I have no experience.

[@cbesthelper404]

@@PureExile Yes, that's the thing. He has experience with different students, some of whom would not appreciate the fact that you can multiply throughout by 2 in order to clear the denominators. So, he has selected to take the route that he did.