Solve the equation. \[ 0.5 x+\frac{4}{5} x=x+3 \]

To solve the equation \( 0.5 x + \frac{4}{5} x = x + 3 \), let's first rewrite the terms on the left side for clarity. Convert \( 0.5 \) to a fraction: \[ 0.5 x = \frac{1}{2} x. \] Now, we have: \[ \frac{1}{2} x + \frac{4}{5} x = x + 3. \] To combine the terms on the left, we'll find a common denominator for \(\frac{1}{2}\) and \(\frac{4}{5}\). The least common multiple of 2 and 5 is 10. Rewriting both terms gives: \[ \frac{1}{2} x = \frac{5}{10} x \quad \text{and} \quad \frac{4}{5} x = \frac{8}{10} x. \] Thus, we have: \[ \frac{5}{10} x + \frac{8}{10} x = x + 3. \] Combining the fractions on the left: \[ \frac{5 + 8}{10} x = \frac{13}{10} x. \] So our equation now reads: \[ \frac{13}{10} x = x + 3. \] Next, we can eliminate \(x\) on the right side by rewriting \(x\) as \(\frac{10}{10} x\): \[ \frac{13}{10} x - \frac{10}{10} x = 3. \] This simplifies to: \[ \frac{3}{10} x = 3. \] To solve for \(x\), multiply both sides by \(\frac{10}{3}\): \[ x = 3 \times \frac{10}{3} = 10. \] Thus, the solution to the equation is: \[ \boxed{10}. \]