When a negatively charged balloon is brought near a neutral wall, the charges in the wall will rearrange. Specifically, the negative charges (electrons) in the wall will be repelled by the negatively charged balloon, causing them to move away from the side of the wall that is closer to the balloon. This leaves behind a region of positive charge (due to the lack of electrons) on the side of the wall that is nearer to the balloon.
Therefore, the correct statement is:
The wall will have its positive charges on the side closer to the balloon.