1. **State the problem:** Solve the equation $$10x = 2.5x$$ and determine how many solutions it has. 2. **Write the equation:** $$10x = 2.5x$$ 3. **Subtract $$2.5x$$ from both sides to isolate terms:** $$10x - 2.5x = 2.5x - 2.5x$$ 4. **Simplify both sides:** $$\cancel{10x} - \cancel{2.5x} = 0$$ which gives $$7.5x = 0$$ 5. **Divide both sides by 7.5 to solve for $$x$$:** $$\frac{7.5x}{7.5} = \frac{0}{7.5}$$ 6. **Simplify:** $$x = 0$$ 7. **Interpretation:** The equation has exactly one solution, $$x=0$$. **Final answer:** One solution, $$x=0$$.