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To find the equations that have infinitely many solutions, we need to identify the ones that are **always true**, regardless of the values assigned to the variables.

Here are the options:

1. **1 = -1**: This is **never true**, so it does not have infinitely many solutions.
2. **3 = 4**: This is also **never true**, so it does not have infinitely many solutions.
3. **c = 1**: This is a specific equation with one solution, not infinitely many.
4. **2x = 2x**: This is **always true**, regardless of the value of \( x \), so it has **infinitely many solutions**.
5. **5 = 5**: This is **always true**, and thus it also has **infinitely many solutions**.
6. **v = 0**: This is a specific equation with one solution (when \( v = 0 \)), so it does not have infinitely many solutions.

Therefore, the correct answers are:
- \( 2x = 2x \)
- \( 5 = 5 \)

Would you like more details on this, or do you have any further questions?

Here are 5 related questions you might find useful:
1. What conditions lead to infinitely many solutions in a system of equations?
2. What types of equations have no solutions?
3. How can we tell if a linear equation has a unique solution?
4. What happens when the coefficients on both sides of an equation are equal?
5. How do contradictions, like \( 3 = 4 \), affect the number of solutions?

**Tip**: An equation that simplifies to a form like \( 0 = 0 \) is a sign of infinitely many solutions.

I solved an equation and found infinitely many solutions. Which of these could be my answer? SELECT ALL THAT APPLY

Explore which equations such as '2x = 2x' and '5 = 5' inherently have infinitely many solutions due to their identity nature, suitable for students in Grades 7-12.

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