1. The problem is to simplify the expression $$d = 1 + \frac{3}{5} : 2x - \frac{4}{3}$$. 2. The colon ":" here means division, so rewrite the expression as $$d = 1 + \frac{\frac{3}{5}}{2x} - \frac{4}{3}$$. 3. Write the division as multiplication by the reciprocal: $$d = 1 + \frac{3}{5} \times \frac{1}{2x} - \frac{4}{3}$$. 4. Multiply the fractions: $$\frac{3}{5} \times \frac{1}{2x} = \frac{3}{10x}$$. 5. Substitute back: $$d = 1 + \frac{3}{10x} - \frac{4}{3}$$. 6. To combine the constants 1 and $$-\frac{4}{3}$$, write 1 as $$\frac{3}{3}$$: $$d = \frac{3}{3} + \frac{3}{10x} - \frac{4}{3}$$. 7. Combine $$\frac{3}{3} - \frac{4}{3} = \frac{3 - 4}{3} = -\frac{1}{3}$$. 8. Final simplified expression: $$d = -\frac{1}{3} + \frac{3}{10x}$$. This is the simplified form of the expression for $$d$$.