Discussion

Question:

The smallest integer x for which the inequality $\frac{x - 7}{x^{2} + 5 x - 36} > 0 is given by$

Explanation:

The LHS is of the form: (x – 7) / (x + 9) (x – 4)

For x > 7, the expression will be positive.

Similarly, for any negative integer,

[(x – 7)/(x – 4)] will always be positive.

For the expression to be positive,

(x + 9) > 0 i.e. x > −9

Hence, the smallest integer that satisfies this inequality is x = −8

Hence, option (d)

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