Question

HELP HELP!!
solve the following inequality.

(x-4)(x-5)(x-6)<0
(put answer into interval notation)

The solution set is________
OR
There is no solution.

Answer 1

It is best to make a sign scheme. This is a number line on which you mark the zeros.
Because the zeros are 4, 5 and 6 (just plug these numbers in to see it!), you get this:


This divides the number line into 4 different parts.
If you try another number, say 3, you can see what (x-4)(x-5)(x-6) will be:
(3-4)(3-5)(3-6)=-1 * -2 * -3 = -6 < 0. This is what we are looking for!

So the area left of x=4 is part of the solution. Let's put "-" signs there:

Answer 2

okay? i understand so far.

Answer 3

Trying out other numbers gives this result:
Can you see all the parts of the number line that are part of the solution?

Answer 4

Oops, the spacing of the --- and +++ has gone wrong!

Answer 5

It should be
---- left of 4,
++++ between 4 and 5
------ between 5 and 6,
++++ right of 6.

Answer 6

So (x-4)(x-5)(x-6)<0 for \(x \in (-\infty, 4) \cup (5,6) \).

Answer 7

okay thank you sOOO much!! had no clue on how to do now I do!!

Answer 8

If the inequality is aready in factored form (as was this one) then all you have to do is make that sign scheme and read off the solution!