1. **State the problem:** Simplify the expression $$3 + 4 - 1 + 3x - 2x + 4x$$. 2. **Combine like terms:** Group the constant terms and the terms with $x$ separately. Constants: $$3 + 4 - 1$$ Terms with $x$: $$3x - 2x + 4x$$ 3. **Simplify constants:** $$3 + 4 - 1 = 7 - 1 = 6$$ 4. **Simplify $x$ terms:** $$3x - 2x + 4x = (3 - 2 + 4)x = 5x$$ 5. **Write the simplified expression:** $$6 + 5x$$ **Final answer:** $$6 + 5x$$