1. The problem asks whether "all real solutions" is ever an option when solving an absolute value equation or inequality. 2. Recall that an absolute value equation or inequality involves expressions like $|x| = a$ or $|x| < a$ where $a$ is a real number. 3. Important rule: The absolute value $|x|$ is always non-negative, so equations or inequalities involving absolute values have solutions only if the conditions make sense (e.g., $|x| = -1$ has no solution). 4. When solving absolute value equations or inequalities, the solution set can be empty, a finite set, or an interval, but it cannot be "all real numbers" unless the inequality is always true. 5. For example, $|x| eq 0$ excludes zero, so not all real numbers are solutions. 6. However, consider $|x| \\geq 0$, which is true for all real $x$, so the solution set is all real numbers. 7. Therefore, "all real solutions" can be an option for absolute value inequalities that are always true. 8. Hence, the statement "all real solutions is never an option" is False. Final answer: False