Question

HELPP! this is my second time uploading this question:,,)

George tells you that when variables are in the denominator, the equation
2/3+5/x=8/9 becomes unsolvable. George explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to George how the equation is still solvable and explain your reasoning.

Answer 1

X can equal 22.5

Explanation:

I've set up the equation below:

`(2)/(3) +(5)/(x) =(8)/(9)`

With this equation, as any addition equation goes, we assume it to be like this:

A + B = C

so

C - A = B

that means,

`(8)/(9) -(2)/(3) =(5)/(x)`

The easiest thing to do is to make 2/3 have the same denominator as 8/9, we do this by...

`(2)/(3) *(3)/(3) = (6)/(9) \\`

So...

`(8)/(9) -(6)/(9) =(2)/(9) =(5)/(x)`

We now know that 5 over x equals 2 over nine. We can determine x by cross multiplying as follows:

`(5)/(x) =(2)/(9) \\2x = 45\\x=22.5`

So, x is 22.5, making the equation indeed solvable.

Have a nice day, fam. This problem really worked my brain! Spread The Love.