Let's solve the equation step by step:

$3(2 + u) - u = 6 + 2(u + 1)$

Step 1: Distribute both sides

Distribute the constants inside the parentheses.

$3 \cdot 2 + 3 \cdot u - u = 6 + 2 \cdot u + 2$

This simplifies to:

$6 + 3u - u = 6 + 2u + 2$

Step 2: Simplify both sides

Now, combine like terms.

On the left side: $6 + (3u - u) = 6 + 2u$

On the right side: $6 + 2u + 2 = 8 + 2u$

So the equation becomes: $6 + 2u = 8 + 2u$

Step 3: Eliminate the variable $2u$

Subtract $2u$ from both sides:

$6 = 8$

Step 4: Identify the result

This is a contradiction. The equation $6 = 8$ is not true, which means the original equation has no solution.

Conclusion:

The equation has no solution because we reached a contradiction during the simplification process.

Would you like further clarification or help with any other math questions?

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Here are some related questions you could explore:

1. What does it mean when an equation has no solution?
2. How can you identify contradictions in equations?
3. How do you solve an equation with absolute values?
4. What are some types of systems of equations and how do you solve them?
5. How do you check the solution to an equation once you find it?

Tip: Always check for contradictions during simplification; if you end up with a false statement (like 6 = 8), the equation has no solution.