1. **State the problem:** Solve the equation $$6x - 2x - 1 = 3x + 5$$ for $x$. 2. **Combine like terms on the left side:** $$6x - 2x = 4x$$ So the equation becomes: $$4x - 1 = 3x + 5$$ 3. **Isolate variable terms on one side:** Subtract $3x$ from both sides: $$4x - 3x - 1 = 3x - 3x + 5$$ $$\cancel{4x} - \cancel{3x} - 1 = 0 + 5$$ $$x - 1 = 5$$ 4. **Isolate $x$ by adding 1 to both sides:** $$x - 1 + 1 = 5 + 1$$ $$x = 6$$ 5. **Final answer:** $$\boxed{6}$$