Question 647543
{{{abs(z-2) > 0 }}} = {{{(z-2) >0}}} and {{{-(z-2) > 0}}}
i)
{{{z-2>0}}}
{{{z > 2}}}
ii)
{{{-(z-2)>0}}}
Recall when dividing or multiplying by a negative number, it switches the way the inequality points.
{{{(z-2)<0}}}
{{{z<2}}}

So we have that z<2 and z>2. The answer may be clearer if we put this in interval notation.

So z exists in  (-infinity,2) U (2,infinity). U is the union of sets symbol.

D.