Which of the following equations have no solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)   
\[29x+29=29x-11\]
A
\[29x+29=29x-11\]
(Choice B)   
\[29x+92=29x-11\]
B
\[29x+92=29x-11\]
(Choice C)   
\[29x+11=29x-11\]
C
\[29x+11=29x-11\]
(Choice D)   
\[29x-29=29x-11\]
D
\[29x-29=29x-11\]

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.

---

### Choice B:
\[
29x + 92 = 29x - 11
\]
Subtract \(29x\) from both sides:
\[
92 = -11
\]
This is also a contradiction, so **Choice B** has no solutions.

---

### 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.

---

### Choice D:
\[
29x - 29 = 29x - 11
\]
Subtract \(29x\) from both sides:
\[
-29 = -11
\]
This is a contradiction too, so **Choice D** has no solutions.

---

### 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.

---

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.

Which of the following equations have no solutions? Choose all answers that apply:
A. 29x + 29 = 29x - 11
B. 29x + 92 = 29x - 11
C. 29x + 11 = 29x - 11
D. 29x - 29 = 29x - 11

This problem helps students determine which of the given linear equations have no solutions by simplifying both sides and checking for contradictions. It covers algebraic concepts suitable for Grades 6-8, including solving and analyzing linear equations.

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