x-3/20=4/5-1/2

To solve the equation \( \frac{x - 3}{20} = \frac{4}{5} - \frac{1}{2} \), we first need to simplify the right side:

1. Find a common denominator for the fractions on the right side. The common denominator for 5 and 2 is 10.

   • Convert \( \frac{4}{5} \) to have a denominator of 10: \[ \frac{4}{5} = \frac{4 \cdot 2}{5 \cdot 2} = \frac{8}{10} \]

   • Convert \( \frac{1}{2} \) to have a denominator of 10: \[ \frac{1}{2} = \frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10} \]

2. Now, subtract \( \frac{5}{10} \) from \( \frac{8}{10} \): \[ \frac{8}{10} - \frac{5}{10} = \frac{8 - 5}{10} = \frac{3}{10} \]

Now the equation becomes: \[ \frac{x - 3}{20} = \frac{3}{10} \]

3. To eliminate the fraction, multiply both sides by 20: \[ x - 3 = 20 \cdot \frac{3}{10} \]

Calculating the right side: \[ 20 \cdot \frac{3}{10} = 2 \cdot 3 = 6 \]

Now the equation is: \[ x - 3 = 6 \]

4. Finally, add 3 to both sides to solve for \( x \): \[ x = 6 + 3 = 9 \]

Thus, the solution is: \[ \boxed{9} \]