1. **State the problem:** Solve the equation $$\frac{3}{2}x - 2.5 = 5 + 0.25x$$. 2. **Write the formula and rules:** To solve linear equations, isolate the variable $x$ by moving all terms involving $x$ to one side and constants to the other. 3. **Step 1: Move $0.25x$ to the left side:** $$\frac{3}{2}x - 0.25x - 2.5 = 5$$ 4. **Step 2: Simplify the left side:** Convert $\frac{3}{2} = 1.5$, so $$1.5x - 0.25x - 2.5 = 5$$ $$1.25x - 2.5 = 5$$ 5. **Step 3: Move $-2.5$ to the right side:** $$1.25x = 5 + 2.5$$ $$1.25x = 7.5$$ 6. **Step 4: Solve for $x$ by dividing both sides by $1.25$:** $$x = \frac{7.5}{1.25}$$ Show cancellation: $$x = \frac{\cancel{7.5}}{\cancel{1.25}} \times \frac{6}{6} = \frac{45}{6}$$ Simplify fraction: $$x = \frac{15}{2} = 7.5$$ 7. **Final answer:** $$\boxed{7.5}$$