My first question is, if there's a problem, for example like:

(x+2)(2x-1)=0
would the answer be -2 and 1/2 or would it be -2 or 1/2???






And my second question is how do you solve this type of question in less than 15 seconds?

Solve |x-2|>|x-8|

not sure why you're even asking the first question. serious question, is english not your native language?

if you're asking about semantics, then you need to give the question. there is no "answer" to an equation, only a set of solutions. and the set is {-2, 1/2}. i do not know why you insist on using the english words "and" and "or"

for your second question, look at the edge cases. clearly it's never the case when x >= 8. so set both of them to 0 and look inside the intervals.

if you do not want to use the set notation given by "carteblanche" use 'both -2 and 1/2'

for abs(x-2) > abs(x-8) you could just graph the two sides and you see where the lines cross
but a quick calculation [just divide 2+8 by 2] shows that when x=5 we have abs(5-2) = abs (5-8)
one can also see that when x is larger than 5 the inequality abs(x-2) > abs(x-8) will always hold
(for x less than 5 it's the other way round)