SOLUTION: Solve the following inequality (x-4)(x-5)(x-6)>0 The solution set_____

SOLUTION: Solve the following inequality (x-4)(x-5)(x-6)>0 The solution set______ (interval notation)

Question 755723: Solve the following inequality (x-4)(x-5)(x-6)>0
The solution set______ (interval notation)
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The factored form as you have is very convenient for finding the solution set. The critical values are at x equal to 4, 5, and 6. The intervals to check are these:

(-infin, 4)
(4, 5)
(5, 6)
(6, +infin)

Test -5. Let x = -5.
(-)(-)(-)=(-)<0? TRUE.

Test 4.5
(+)(-)(-)=(+)<0? FALSE

Test 5.5.
(+)(+)(-)=(-)<0? TRUE.

Test x=7.
(+)(+)(+)=(+)<0? FALSE.

Each of those tests correspond to the item corresponding to the listed intervals.
Solution set is (-infin, +4) AND (+5, +6).

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