An absolute value measures an expression's distance from a midpoint on a number line.
|x+4|= 9
This equation means that the distance is 9, either in the positive direction or the negative direction.
|x+4|= 9 ⇒ lx+4= 9 x+4= - 9
Since we are interested in the negative solution of the equation, we need to solve the second case for x.