# How do you solve the absolute value inequalities abs(x+4)<0?

Apr 24, 2015

By solve the inequality, I assume you mean solve for $x$. In general you can only solve an equation or inequality for "something",

For the given inequality: $\left\mid x + 4 \right\mid < 0$
Note that
$\left\mid \text{anything} \right\mid \ge 0$
(it's basic to the definition of absolute value)

Therefore there is no value of $x$ for which this inequality is true.

In set notation
$x = \phi \text{ (the null set) }$