1. **State the problem:** Solve the equation $$\frac{9}{6x} + 2 - 3 = 25$$ for $x$. 2. **Simplify the equation:** Combine like terms on the left side: $$2 - 3 = -1$$ So the equation becomes: $$\frac{9}{6x} - 1 = 25$$ 3. **Isolate the fraction:** Add 1 to both sides: $$\frac{9}{6x} = 25 + 1 = 26$$ 4. **Solve for $x$:** Multiply both sides by $6x$ to clear the denominator: $$9 = 26 \times 6x$$ $$9 = 156x$$ 5. **Divide both sides by 156:** $$x = \frac{9}{156}$$ 6. **Simplify the fraction:** Both numerator and denominator are divisible by 3: $$x = \frac{3}{52}$$ **Final answer:** $$x = \frac{3}{52}$$