Question 1029913: For what values of x is it true that x^2 - 5x - 4 <= 10? Express your answer in interval notation.
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! From
x^2 - 5x - 4 <= 10
subtract ten and then factor it...
x^2 - 5x - 14 <= 0
(x - 7)(x + 2) <= 0
For the product to be less than zero, it means that one factor must be positive and the other must be negative.
Normally I teach students to put on the number line at 7 and at -2 and then
ask them to see which of the three intervals works...
Greater than 7 makes the both positive (so that doesn't work).
Less than -2 makes them both negative (so that doesn't work).
The interval that works is between -2 and 7, inclusive, so our answer is
[-2,7]
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