Solve for X: Combining Fractions 2/3x + 1/4x - 1/5x + 1/2x = 2

To solve for $x$ in the equation $\frac{2}{3}x+\frac{1}{4}x-\frac{1}{5}x+\frac{1}{2}x=2$, we will follow these steps:

Step 1: Combine the coefficients of $x$ by finding a common denominator.
- The denominators are 3, 4, 5, and 2. The least common multiple (LCM) of these is 60.
- Rewrite each term with a denominator of 60:
$\frac{2}{3}x = \frac{40}{60}x$, $\frac{1}{4}x = \frac{15}{60}x$, $\frac{1}{5}x = \frac{12}{60}x$, $\frac{1}{2}x = \frac{30}{60}x$.

Step 2: Combine the fractions:
- Combine to get: $\frac{40}{60}x + \frac{15}{60}x - \frac{12}{60}x + \frac{30}{60}x = \frac{73}{60}x.$

Step 3: Set up the equation and solve for $x$:
- The equation becomes $\frac{73}{60}x = 2$.
- Multiply both sides by $\frac{60}{73}$ to isolate $x$:
$x = 2 \times \frac{60}{73}$.

Therefore, $x = \frac{120}{73}$.