Note the absolute value. When is the absolute value of a quantity greater than or equal to $−4$?

all real numbers

Rewrite the inequality as an equation, factor, and solve for $x$. Since this is an inequality, these are the boundary points.

$(x−4)(x+5)=0$
The boundary points are $4$ and $−5$.

Plot your boundary points on a number line. Test a point in each region to see which region(s) make the inequality true.

$−5<x<4$