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

$\frac{4}{5}+\frac{3}{x}=\frac{1}{2}$

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

$\frac{4}{5}\cdot10x+\frac{3}{x}\cdot10x=\frac{1}{2}\cdot10x$

simplify

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

therefore

The equation is solvable