Answer :
Let's analyze each of the given equations step by step and determine which ones have infinitely many solutions.
For an equation to have infinitely many solutions, both sides of the equation must be identical, meaning that they are equal for any value of \( x \).
### Equation A: \( 73x - 37 = 73x - 37 \)
- Both sides of the equation are \( 73x - 37 \).
- Since the expressions on both sides are identical regardless of the value of \( x \), this equation has infinitely many solutions.
### Equation B: \( 37x - 37 = 37x - 37 \)
- Both sides of the equation are \( 37x - 37 \).
- Since the expressions on both sides are identical regardless of the value of \( x \), this equation has infinitely many solutions.
### Equation C: \( 74x - 37 = 74x - 37 \)
- Both sides of the equation are \( 74x - 37 \).
- Since the expressions on both sides are identical regardless of the value of \( x \), this equation has infinitely many solutions.
### Equation D: \( x - 37 = x - 37 \)
- Both sides of the equation are \( x - 37 \).
- Since the expressions on both sides are identical regardless of the value of \( x \), this equation has infinitely many solutions.
To summarize, all of the provided equations have infinitely many solutions. Therefore, the correct answers are:
- A. \( 73x - 37 = 73x - 37 \)
- B. \( 37x - 37 = 37x - 37 \)
- C. \( 74x - 37 = 74x - 37 \)
- D. \( x - 37 = x - 37 \)
So the correct choices are all of the above: A, B, C, and D.
For an equation to have infinitely many solutions, both sides of the equation must be identical, meaning that they are equal for any value of \( x \).
### Equation A: \( 73x - 37 = 73x - 37 \)
- Both sides of the equation are \( 73x - 37 \).
- Since the expressions on both sides are identical regardless of the value of \( x \), this equation has infinitely many solutions.
### Equation B: \( 37x - 37 = 37x - 37 \)
- Both sides of the equation are \( 37x - 37 \).
- Since the expressions on both sides are identical regardless of the value of \( x \), this equation has infinitely many solutions.
### Equation C: \( 74x - 37 = 74x - 37 \)
- Both sides of the equation are \( 74x - 37 \).
- Since the expressions on both sides are identical regardless of the value of \( x \), this equation has infinitely many solutions.
### Equation D: \( x - 37 = x - 37 \)
- Both sides of the equation are \( x - 37 \).
- Since the expressions on both sides are identical regardless of the value of \( x \), this equation has infinitely many solutions.
To summarize, all of the provided equations have infinitely many solutions. Therefore, the correct answers are:
- A. \( 73x - 37 = 73x - 37 \)
- B. \( 37x - 37 = 37x - 37 \)
- C. \( 74x - 37 = 74x - 37 \)
- D. \( x - 37 = x - 37 \)
So the correct choices are all of the above: A, B, C, and D.
