The statement x^2-x-6<0 is equivalent to the statement:

1965 AMC 12 Problem 10

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10.

The statement

x^2-x-6\lt0

is equivalent to the statement:

-2\lt x\lt3

x\gt-2

x\lt3

x\gt3

and

x\lt-2

x\gt3

x\lt-2

Factor

x^2-x-6

A positive-leading quadratic is negative between its two roots

We have

x^2-x-6=(x-3)(x+2).

This product is negative exactly between its roots, so

-2\lt x\lt3.

Therefore, the correct answer is A.