The problem asks, "Which of the following equations have no solutions?" The equations provided are:

• A: $29x + 92 = 29x - 11$
• B: $29x + 11 = 29x - 11$
• C: $29x - 29 = 29x - 11$
• D: $29x + 29 = 29x - 11$

To find which equations have no solutions, we can analyze them one by one.

A: $29x + 92 = 29x - 11$

Subtracting $29x$ from both sides: $92 = -11$ This is a contradiction, so A has no solutions.

B: $29x + 11 = 29x - 11$

Subtracting $29x$ from both sides: $11 = -11$ This is also a contradiction, so B has no solutions.

C: $29x - 29 = 29x - 11$

Subtracting $29x$ from both sides: $-29 = -11$ This is a contradiction, so C has no solutions.

D: $29x + 29 = 29x - 11$

Subtracting $29x$ from both sides: $29 = -11$ This is another contradiction, so D has no solutions.

Conclusion:

All the equations A, B, C, and D have no solutions.

Would you like more details on how to handle such contradictions, or do you have any other questions?

Here are 5 questions that build on this:

1. What are the general conditions for an equation to have no solutions?
2. How do equations with no solutions differ from those with infinite solutions?
3. Can a system of linear equations also have no solutions? If so, why?
4. How can you identify equations that have infinite solutions?
5. What happens when you subtract variables from both sides, and how can you identify contradictions earlier?

Tip: Equations with no solutions often simplify to a false statement like $c = d$, where $c$ and $d$ are constants and $c \neq d$.