what is the value of X ? | A nice factorial equation to solve

#short
#youtubeshort
#maths
#simple equation
#proof
#algebra

in this video we are going to fine the value of x From this equation

[ChaosNe]

5!/2=(5•4•3•2•1)/2=5•4•3•1=60
2.5!=3.32335097 (using the Gamma-Function)
60 is not equal to 3.32335097. You cannot just divide the 5 out of the term 5!.


The correct way to do this would be to:
1. Find y in y!=120, which y=5
2. Find x in (2x+4)!=5! (without dividing by 2, because now you can actually lose the factorial!)
Which is equivalent to finding x in 2x+4=5 which results in x=0.5

I honestly don't know why you insisted on dividing by 2 early.

[russelljames]

Once you knew it was 5, you could set 2x plus 4 equal to 5 and solve...why the long way around?

[faming]

The real challenge here is to find n for n!=120. Getting x from there is trivial.
Yet the video spends no time how to do a reversed factorial; it just says oh you know 120=5x4x3x2x1=5!. Then it spends the remaining 2:28 to calculate (5-4)/2 and show the result is correct.

What if the question was to find n for n!=479001600 or n!=√π?
(BTW, they both have a rational solution!)

[joeschmo]

Too complicated. 2x+4=5, 2x=1, x = 0.5.
No need to divide by 2 to isolate x, just pull the constants to one side first.