Question 104

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

Solution

$$\frac{x-7}{x^2 + 5x-36}$$ > 0

$$\frac{x-7}{(x+9)(x-4)}$$ > 0

So $$x \epsilon (-9,4) U (7, \infty$$)

So smallest integer in this range is $$x = -8$$.