pH of water (h+)=(oh-) ??

Approaching this question; there are two things I am completely confused about. Firstly , does the water having a pH of 7 mean that it is neutral and therefore [H+] = [OH-]? If so, does that mean that the water in this question having a pH of 7.47 mean that the hydrogen ion concentration does not equal the hydroxide ion concentration? Because in the working out for the answer to calculate the ionic product of water; they take [H+] to be equal to [OH-]; which I thought only applies to pure water with a pH of 7.

If you take a look at the water dissociation reaction:

H₂O <-> H⁺ + OH^-

amount of H⁺ produced must be equal to amount of OH^- produced, and their concentration are identical (assuming there are no other sources of H⁺ and OH^-). Neutral water doesn't mean pH of 7 - it means equal concentrations of H⁺ and OH^-. Depending on the temperature pH of neutral water changes, see table here.

Consider pure water at 5 degrees vs 70 degrees. The water is always neutral but because the extent of autoionisation will have changed due to the temperature change he pH will have changed.