range of expression

if (3 - x)(6 - x) <=0

find the range of values of x for which this expression is true.







Answer
this is only possible when
case 1. (3 - x) is -ve and (6 - x) is +ve, because -ve x +ve = -ve
case 2. (3 - x) is +ve and (6 - x) is -ve, because -ve x +ve = -ve

case 1.
3 - x <= 0 => x >= 3,
6 - x > = 0 => x =< 6

so, 3 =< x =< 6

similarly solve case 2.

3 - x > = 0 => x =< 3,
6 - x  <= 0 => x >= 6
 
 so, 3 =< x => 6, as you may notice this condition cannot be fulfilled, so
answer: 3 =< x =< 6