Question

19.Solve the inequality. Express your answer in the form of a graph and in interval notation. (x-3) / (x+6) ≤ 0

Answer 1

The inequality is given as,

`(x-3)/(x+6)\leq0`

Note that the denominator can never be zero otherwise the rational function would become indeterminate. So we have to exclude the value at which the denominator,

`\begin{gathered} x+6=0 \\ x=-6 \end{gathered}`

So the function is not defined at x = - 6.

Consider that the division of the numbers can be non-positive, only if exactly one of the numbers is non-positive.

So we have to obtain the interval in which one of the factors is positive and the other is negative.

CASE-1: When the numerator is positive and the denominator is negative,