you may want another opinion but since your answer must be not equal to zero and also cannot be negative you have to look at the (x-7) portion. you cannot just say all real numbers are greater than zero, because if you plug 7 into the problem, then (7-7) = 0 and will make the rest wrong, also if you plugged 5 into the problem (5-7) you would get a negative number, once again making it wrong. to solve the equation you have to set each one to grater than zero (you can graph after to help see) so x+6>0 ='s x>-6, x-7>0 ='s x>7 and x+4>0 ='s x>-4. the only answer that will work is that x is all real numbers greater than but not equal to 7 or (7,infinity).
