Intermediate Algebra: Connecting Concepts through Application

$\bf{\text{Solution Outline:}}$ 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 $\text{ no solution .}$