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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.

User Bumble
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1 Answer

5 votes

Answer:

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.

User Mir Rahed Uddin
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