Question

George tells you that when variables are in the denominator, the equation four over five plus three over x equals one over two 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

Explanation:

The equation is still solvable and the denominator will not become zero as:

Consider the given equation,

`(4)/(5)+(3)/(x)=(1)/(2)`

⇒
`(3)/(x)=(1)/(2)-(4)/(5)`

⇒
`(3)/(x)=(5-8)/(10)`

⇒
`(3)/(x)=(-3)/(10)`

⇒
`-3x=10{*}3`

⇒
`-3x=30`

⇒
`x=-10`

Answer 2

Answer
This explanation shows that the equation is solvable and there is not where in the steps we get a zero on the denominator.


Explanation
The equation given in the statement is;
4/5+3/x=1/2
This equation can be solved as follows:
4/5+3/x=1/2
3/x=1/2-4/5=(5-8)/10
3/x= -3/10
Taking the reciprocal on both side of the equation;
x/3=-10/3
Multiplying by 3 both sides we get;
x= -10