Solve the equation: \((9x)/(2) + 1 = (7x)/(8) + 3\)

Subtract $\frac{7x}{8}$ from both sides:

$$\frac{9x}{2} - \frac{7x}{8} + 1 = 3$$

Subtract 1 from both sides:

$$\frac{9x}{2} - \frac{7x}{8} = 3 - 1$$ $$\frac{9x}{2} - \frac{7x}{8} = 2$$

The least common multiple (LCM) of 2 and 8 is 8.
Rewrite the fractions with the common denominator:

$$\frac{9x \cdot 4}{2 \cdot 4} - \frac{7x}{8} = 2$$ $$\frac{36x}{8} - \frac{7x}{8} = 2$$

$$\frac{36x - 7x}{8} = 2$$ $$\frac{29x}{8} = 2$$

Multiply both sides by 8:

$$29x = 2 \cdot 8$$ $$29x = 16$$

Divide both sides by 29:

$$x = \frac{16}{29}$$

The final answer is $\frac{16}{29}$.