1. **State the problem:** Solve the equation $$\frac{x - 1}{2} + 3x = 10$$. 2. **Formula and rules:** To solve linear equations, combine like terms and isolate the variable on one side. 3. **Step 1:** Multiply both sides by 2 to eliminate the denominator: $$2 \times \left(\frac{x - 1}{2} + 3x\right) = 2 \times 10$$ which simplifies to $$x - 1 + 6x = 20$$. 4. **Step 2:** Combine like terms: $$7x - 1 = 20$$. 5. **Step 3:** Add 1 to both sides: $$7x = 21$$. 6. **Step 4:** Divide both sides by 7: $$x = 3$$. **Final answer:** $$x = 3$$.