Solve for X: x + 2x/4x + 1/2 - 1/3 = 2x Algebraic Equation

To solve the problem, we will follow these steps:

• Step 1: Simplify the fraction $\frac{2x}{4x}$.
• Step 2: Combine like terms on both sides of the equation.
• Step 3: Solve for $x$ using algebraic operations.

Now, let's work through each step:

Step 1: Simplify the fraction.
The term $\frac{2x}{4x}$ simplifies to $\frac{1}{2}$ because the $x$ terms cancel out, clearly assuming $x \neq 0$.

Step 2: Substitute and combine like terms.
The original equation becomes:

$x + \frac{1}{2} + \frac{1}{2} - \frac{1}{3} = 2x$

This simplifies further by combining $\frac{1}{2} + \frac{1}{2} = 1$, so:

$x + 1 - \frac{1}{3} = 2x$

Simplify $1 - \frac{1}{3}$ to $\frac{2}{3}$, yielding:

$x + \frac{2}{3} = 2x$

Step 3: Solve for $x$.
Subtract $x$ from both sides to isolate terms involving $x$:

$\frac{2}{3} = 2x - x$

Simplifying, we have:

$\frac{2}{3} = x$

Therefore, the value of $x$ that satisfies the equation is $\frac{2}{3}$.