Final answer:
Only equation C) -75x + 57 = -75x + 57 has infinitely many solutions because after simplifying both sides, the equation reduces to a true statement (57 = 57) that is valid for all values of x.
Step-by-step explanation:
The student has asked which of the following equations have infinitely many solutions:
- A) 75x + 57 = -75x + 57
- B) 57x + 57 = -75x - 75
- C) -75x + 57 = -75x + 57
- D) -57x + 57 = -75x + 75
An equation has infinitely many solutions when both sides are identical after simplifying. Looking at the options provided, only option C) has this property. When you subtract -75x from both sides of equation C), you are left with 57 = 57, which is true for all values of x. Therefore, equation C) is the one with infinitely many solutions.