Question

x+2/x+3<0
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.

Answer 1

\[ \frac{x+2}{x+3}< 0 \]
How were you taught to do this type of problem?
one way to solve it is to know you want the expression to be negative (because "less than zero" means negative)

to get a negative expression, you need either
1) top + and bottom - or
2) top - and bottom +
(because you need opposite signs)

Test option 1) top + means top bigger than 0: x+2 > 0 --> x> -2
at the same time we need the bottom to be negative. x+3<0 x< -3
we see we need x to be bigger than -2 and at the same time, smaller than -3
this is not possible.

now check option 2