Question

George feels you that when variables are in the denominator, the equation 4/5 + 3/x = 1/2 becomes unsolvable. George explains “there is a value for x that makes the denominator 0 and you can’t divide by 0.” Demonstrate to George how the equation is still solvable, and explain your reasoning.

Answer 1

we have the equation

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

Remember that the value of x cannot be equal to zero, because the denominator cannot be equal to zero

Simplify the expression

Multiply both sides by 10x

`(4)/(5)\cdot10x+(3)/(x)\cdot10x=(1)/(2)\cdot10x`

simplify

`\begin{gathered} 8x+30=5x \\ 8x-5x=-30 \\ 3x=-30 \\ x=-10 \end{gathered}`

therefore

The equation is solvable