1. **State the problem:** Solve the equation $$6x - 7 = 14 - x$$. 2. **Write down the formula and rules:** To solve linear equations, we aim to isolate the variable $x$ on one side by performing the same operations on both sides. 3. **Add $x$ to both sides to get all $x$ terms on one side:** $$6x - 7 + x = 14 - x + x$$ which simplifies to $$7x - 7 = 14$$ 4. **Add 7 to both sides to isolate the term with $x$:** $$7x - 7 + 7 = 14 + 7$$ which simplifies to $$7x = 21$$ 5. **Divide both sides by 7 to solve for $x$:** $$\frac{\cancel{7}x}{\cancel{7}} = \frac{21}{7}$$ which simplifies to $$x = 3$$ 6. **Final answer:** $$x = 3$$