for what positive values of x will x18 be equal to x20?

Question

for my sons math homework

Answer 1

By x18 and x20 I am assuming you mean 18x and 20x. (Some of these homework problems have me wondering if the textbooks these days are presenting variables in new, non-traditional ways or if the people writing them just don't know how to write them!)

At any rate, the only possible value of x where 18x = 20x would be if x = 0. It's truly the "trivial" case, in the classic, mathematical sense of the word.

What class or grade is your son in? And what is your educational background, dad, that you couldn't see this answer yourself? Not trying to knock you, but gosh this was pretty minor.

Well, good luck to both you and your son!

Answer 2

I'm going to assume you mean the 18 and 20 to be exponents. We'd usually write them as x^18 and x^20. This can be solved by inspection, but the better way is to set up the equation and solve it.

x^20 = x^18

x^20 - x^18 = 0

Factor this:

x^18(x^2 - 1) = 0

x^18(x+1)(x-1) = 0

So by the zero property,

x^18 = 0 or x+1 = 0 or x-1 = 0

x = 0, -1 or 1 - pick any of the three.

There's more that can be said about multiple roots and all, but I suspect this is what you need.

Answer 3

maybe im missing something here...but if you have a number 'x'...and take that number and multiply it by 18 and 20...it will never be equal...20 times anything will always be greater than 18 times the same thing???

the only way they would be equal was if x were 0...

(and the above 10/9, 9/10 is incorrect...fyi)

Answer 4

Can only be 0

Answer 5

10/9 or 9/10

Answer 6

If you mean for what values of x would 18 x = 20x, then it's only zero. It's impossible to have any other value.