To determine which equations have no solutions, we can simplify each equation and check whether they lead to a contradiction.

Choice A:

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

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Choice B:

$29x + 92 = 29x - 11$ Subtract $29x$ from both sides: $92 = -11$ This is also a contradiction, so Choice B has no solutions.

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Choice C:

$29x + 11 = 29x - 11$ Subtract $29x$ from both sides: $11 = -11$ This is a contradiction as well, so Choice C has no solutions.

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Choice D:

$29x - 29 = 29x - 11$ Subtract $29x$ from both sides: $-29 = -11$ This is a contradiction too, so Choice D has no solutions.

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Conclusion:

All of the given equations lead to contradictions and therefore have no solutions. Thus, the correct answer is:

• Choice A
• Choice B
• Choice C
• Choice D

Let me know if you need any more details or have any questions.

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Here are 5 related questions to expand on this:

1. How do you determine if an equation has no solutions?
2. What does it mean for two sides of an equation to lead to a contradiction?
3. Can you provide an example of an equation with infinite solutions?
4. What is the difference between a conditional equation and an identity?
5. How can we solve for variables in equations with multiple terms?

Tip: Always simplify equations step-by-step to reveal contradictions or determine if there is a valid solution.