SOLUTION: For what values of x is it true that x^2 - 5x - 4 <= 10? Express your answer in interval notation.

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]
RELATED QUESTIONS
For what values of$x is the following statement true? 3x-2>(6x+4)+(2x-1) Express your... (answered by MathLover1)

What values of x satisfy |x - 4| + |x + 4| <= 10? Express your answer in interval... (answered by stanbon)

Find all x such that x^2+5x<6. Express your answer in interval notation. (answered by josgarithmetic,MathTherapy)

What values of x satisfy |x - 4| + 2(x + 3) <= 11 + 5|x + 7| + 3x + 8. Express your... (answered by greenestamps)

An expression is well-defined if you can compute its value without any illegal... (answered by ikleyn)

An expression is well-defined if you can compute its value without any illegal... (answered by Fombitz,ikleyn)

Find all values of x in the interval [0, 2π] that satisfy the inequality. (Enter... (answered by lwsshak3)

solve the inequality. write answer in interval notation. 100 < or equal to 10(5x-2) < or (answered by stanbon)