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

Mathematics

1 answer:

dybincka [34]3 years ago

5 0

Answer:

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]

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