Final answer:
The equation with infinitely many solutions is -6x+35=-6x+35, because after simplifying, both sides are identical, which results in the identity 35=35. Option 3 is correct.
Step-by-step explanation:
To determine which of the listed equations have infinitely many solutions, we look for equations where both sides are identical after simplification. Let's analyze each equation:
6x+35=-6x+35: On simplifying, we add 6x to both sides to get 12x+35=35. This does not result in an identity, so it does not have infinitely many solutions.
-6x+35=-6x-35: This has no solutions, because when the -6x terms cancel out, we are left with 35=-35, which is not true.
-6x+35=-6x+35: After eliminating the -6x terms on both sides, we have an identity, 35=35, which means this equation has infinitely many solutions.
6x+35=-6x-35: Simplifying similarly, we'll find that this equation cannot be true for any value of x, since 6x cannot equal -6x unless x=0, and even then, 35 cannot equal -35.
Therefore, the equation with infinitely many solutions is -6x+35=-6x+35.