Hello. The first image is the question, the second image is from the solutions manual. I don't understand why these answers are negative. Anyone have a clue?
Sure. (and Welcome to the PF)
Electric field points from positive charges to negative charges. So the E-field at the first negative charge is pointing inward to that negative charge in all directions. The E-field at the positive charge is pointing away from it in all directions. They ask for the sum of the two E-fields at a point between them, so both components point to the left, which is the negative direction on the horizontal axis.