Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises - Page 167: 3

$D$

RECALL: For any real number $x$, $|x| \ge 0$. Since the absolute value of any real number is never negative, then any real number satisfies $|x| \gt -7$. Therefore, the solution to the given inequality is the set of all real numbers, the graph of which is the one represented by the one in Option $D$.