For what values of $x$ is it true that $x^2 - 5x - 4 / le 10$? Express your answer in interval notation.

x ∈ [-2, 7]

Step-by-step explanation:

The given equation ...

x^2 - 5x - 4 ≤ 10

can be rewritten as ...

x^2 - 5x - 14 ≤ 0

and factored as ...

(x + 2) (x - 7) ≤ 0

Clearly, the "or equal to" condition will be met when x=-2 and x=7. For values of x between these numbers, one factor is negative and the other is positive. Hence the product will be negative. So, numbers in that interval are the solution set.

x ∈ [-2, 7]