To solve the equation:

$4x - ( -x + 1) + 1 = 6$

Let's simplify step by step:

1. Distribute the negative sign inside the parentheses: $4x + x - 1 + 1 = 6$

2. Combine like terms: $5x = 6$

3. Solve for $x$ by dividing both sides by 5: $x = \frac{6}{5}$

So, the solution is:

$x = \frac{6}{5} \text{ or } x = 1.2$

Do you have any questions or would you like more details on the solution?

Here are 5 related questions to practice:

1. Solve $3x - (-2x + 5) = 12$.
2. Solve $7x - (3x + 4) + 6 = 10$.
3. Simplify and solve: $2x - (-x + 3) - 2 = 5$.
4. Solve $4x - (x - 2) + 3 = 9$.
5. Solve $5x - (2x - 1) = 8$.

Tip: When you see parentheses in an equation, always deal with the signs first, especially if there is a negative sign outside.