Let's analyze and solve each equation in the image.

First Equation

Given: $3(2 + w) - w = 6 + 2(w + 1)$

1. Expand terms: $3 \cdot 2 + 3 \cdot w - w = 6 + 2 \cdot w + 2$ $6 + 3w - w = 6 + 2w + 2$

2. Simplify each side: $6 + 2w = 8 + 2w$

3. Subtract $2w$ from both sides: $6 = 8$

This is a contradiction, meaning there is no solution for $w$.

Second Equation

Given: $4(u + 1) + 5 = 6(u - 1) + u$

1. Expand terms: $4u + 4 + 5 = 6u - 6 + u$

2. Combine like terms: $4u + 9 = 7u - 6$

3. Move terms involving $u$ to one side and constants to the other: $9 + 6 = 7u - 4u$ $15 = 3u$

4. Solve for $u$: $u = 5$

So, the solution for the second equation is $u = 5$.

Summary:

• For the first equation, there is no solution.
• For the second equation, the solution is $u = 5$.

Would you like further details on any steps?

Related Questions

1. How can we determine if an equation has no solution or infinitely many solutions?
2. What are the implications of a contradictory result like $6 = 8$ in an equation?
3. How can we check our solutions for accuracy?
4. Can equations with similar terms but different constants still have solutions?
5. What are other methods to solve linear equations besides expanding and simplifying?

Tip: When simplifying equations, always try to isolate terms involving the variable on one side to make the solution process clearer.