1. **State the problem:** Solve the equation $7x - 1 = 4x + 8$ for $x$. 2. **Write down the equation:** $$7x - 1 = 4x + 8$$ 3. **Isolate the variable terms on one side:** Subtract $4x$ from both sides: $$7x - \cancel{4x} - 1 = \cancel{4x} + 8 - 4x$$ which simplifies to $$3x - 1 = 8$$ 4. **Isolate the constant term:** Add $1$ to both sides: $$3x - 1 + 1 = 8 + 1$$ which simplifies to $$3x = 9$$ 5. **Solve for $x$ by dividing both sides by 3:** $$\frac{3x}{\cancel{3}} = \frac{9}{\cancel{3}}$$ which simplifies to $$x = 3$$ 6. **Final answer:** $$\boxed{3}$$