Question 39877
(x-2)(x-5)<0

Look at the equality (x-2)(x-5)=0
x=2 or x=5

Put two points on a number line: one for 2 the other for 5.
This divides the number line into three sections.
Pick a single value from each of the sections: e.g. 0,3,10
Test each value in the original inequality: e.g.
For 0: (0-2)(0-5)>0; it is not less than 0, therefore that
section is not part of the solution of the inequality.
For 3: (3-2)(3-5)=1(-2)<0
The result is true so that section is part of the solution of
the inequality.
For 10: (10-2)(10-5)=8*5=40
This is not less than zero; section is not part of the solution.
Only the section containing x=3 is the solution.
SOLUTION:
 2<x<5
Cheers,
Stan H.