More students need to learn this way to solve absolute value equations

Learn how to use the definition of the absolute value, i.e. abs(x-a) represents the distance between x and a on the number line, to solve the equation abs(x-5)+abs(x+1)=6. This equation has infinitely many answers but it's not all real numbers!

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#math #algebra #mathbasics

[Mike__B]

I'm not going to lie, as soon as you said "the distance between" I thought you were going to start invoking complex numbers as part of the solution.

[jensraab]

Conceptualizing this sum of "absolute sums" as a combined distance makes a lot of sense!
It's much more satisfying, and easier, than breaking the equation up in three cases and doing the algebra (as I did before watching the video).
Very neat!

[ibrahimali]

i thought you meant that the solutions aren't all real numbers so i was just patiently waiting for a complex solution 😂
my brain wasn't braining

edit: tHaNkS fOr 1

[fizisistguy]

When you can't understand the problem so he lets you visualise it. Best math teacher❤.

[qccdizl]

OMG I FINALLY UNDERSTOOD WHAT I WASNT ABLE TO FOR LIKE A WEEK TYSMM

[MaxCubing]

At the beginning of the video I was thinking like the solutions were complex or something like this, but after I think he kinda "opened" my mind and I remained shocked about this way to understand better absolute value

[qccdizl]

Please can you do more questions related to the modulus function I would really appreciate it!

[jamesgreenwood]

You can also make use of the triangle inequality to get the same result.

[benspahiu]

When you said “it’s not all real numbers”, I thought you meant complex solutions as well. Thinking about the standard norm in the complex plane, I saw that all solutions form an ellipse around the foci -1 and 5 (flat line since the sum of distances is 6). Looking at the comments, I’m not the only one to have noticed this, but still thought it was really neat.

[HD-fywu]

This reminds me of the property of an ellipse. If the right-hand side of the equation is something more than 6, the solution forms an ellipse with its focus at -1 and 5 respectively, where the vertical axis is the imaginary number axis.

[richardhole]

There is discussion in the comments forva solution in the complex plane. Would you do a follow-up and address that, please.

[rajeshpawar]

Can you please make a video on Lagrange interpolation please please please

[magikarpxd]

Can you move the absolute value to the 8? Like from |x-2|=8 to x-2=|8|

[Ricardo_S]

I check wit intervals, the interval (-∞, -1) both absoluts values their negative inside and gives x=-1 but -1 its not on (-∞, -1) (Actually you can include -1 since 0=-0 but well I realized later)

Then [-1, 5)
And you get the negative inside from x-5 but the positive from x+1
You get -x+5+x+1=6 that give us
6=6 so, al the values between [-1, 5) its an answer (in this part was when I realized that 0=-0)

And the las interval was [5, ∞)
That make the both positives than give us
x=5
So [-1, 5)U[5]=[-1, 5]

I didn't check if there are complex solutions

[seventysevensquare]

It's easier to just make a rough graph of it, range of it's solutions will be pretty clear that way.❤

[lobsoff]

It seems to me that it was easier to explain through a graph, if you know what a graph looks like, these are functions, and then the problem is solved orally!

[theupson]

if you want complex solutions, it's an ellipse and the equation is already in the canonical form. if you're some kind of real number degenerate, it's an extremely simple piecewise function

[sachinth]

Feeling proud as I did it in my head and I got it correct 😎😎

[jesusthroughmary]

So this only works when the two "fixed points" are exactly 6 apart?

[nicholasscott]

What if the distance between the two numbers is not equal to the sum of the absolute values, though, like if you had |x-5| + |x+1| =7?