Final answer:
The solution to the inequality |x+3| > -8 is all real numbers, because an absolute value is never negative, and so it is always greater than any negative number.
Step-by-step explanation:
The given inequality is |x+3| > -8. When solving absolute value inequalities, it's important to remember that the absolute value of a number represents its distance from zero on the number line, therefore it is always non-negative. Since the absolute value of any real number cannot be negative, the inequality |x+3| > -8 is true for all real numbers because the left side will always be greater than any negative number.
Hence, the solution to the inequality is B) all real numbers.
It's also important to note that if the inequality was '|x+3| < -8', there would be no solution, because an absolute value cannot be less than a negative number. However, that is not the case here. Inequalities like this one do not require splitting into two cases, as you would for a positive value on the right side of the inequality (e.g., '|x+3| > 8' would require evaluating both 'x+3 > 8' and 'x+3 < -8').