SOLUTION: (x-2)(x-5)<0

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Question 39877: (x-2)(x-5)<0
Found 2 solutions by fractalier, stanbon:
Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website!
On a number line, make dotted points at 2 and at 5. These are your "critical" points.
Now we test points in each of the three intervals to see if those values (and that entire region) make the inequality
(x-2)(x-5)<0
true.
So try x = 1. Does it make the inequality true? No.
Now try x = 3. Now is it true? Yes.
Now try x = 6. Now is it true? No.
Therefore shade in the region between 2 and 5, and state your answer as
2 < x < 5

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
(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 Cheers,
Stan H.