#### Answer

no solution

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|x+3|+15\lt4
,$ isolate first the absolute value expression. Then use the definition of absolute value to analyze the solution.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
|x+3|+15\lt4
\\\\
|x+3|\lt4-15
\\\\
|x+3|\lt-11
.\end{array}
The absolute value of $x,$ written as $|x|,$ is the distance of $x$ from zero. Hence, it is always a nonnegative number. In the same way, the left side of the inequality above is a nonnegative number. This can never be $\text{
less than
}$ the negative number at the right. Hence, there is $\text{
no solution
.}$