Solving the Equation: 1/x - 1/9 = 1/18 - 1/x
Problem Statement
Given the equation:
$\frac{1}{x} - \frac{1}{9} = \frac{1}{18} - \frac{1}{x}$
Simplifying the Equation
Our goal is to solve for $x$. Let's start by simplifying the equation.
First, we can add $\frac{1}{x}$ to both sides of the equation to get:
$\frac{1}{x} - \frac{1}{9} + \frac{1}{x} = \frac{1}{18}$
This simplifies to:
$\frac{2}{x} - \frac{1}{9} = \frac{1}{18}$
Next, we can add $\frac{1}{9}$ to both sides of the equation to get:
$\frac{2}{x} = \frac{1}{18} + \frac{1}{9}$
Solving for x
Now, let's solve for $x$.
$\frac{2}{x} = \frac{1}{18} + \frac{2}{18}$
$\frac{2}{x} = \frac{3}{18}$
$\frac{2}{x} = \frac{1}{6}$
Multiplying both sides by $x$:
$2 = \frac{x}{6}$
Multiplying both sides by $6$:
$12 = x$
Therefore, the solution to the equation is:
$x = 12$
Conclusion
We have successfully solved for $x$ and found that $x = 12$.
