Solve |a|-|18-9|+|4|<0: Multiple Absolute Value Inequality Analysis

To solve this problem, we need to work through the nested absolute values systematically and then solve the resulting inequality.

Step 1: Simplify the innermost absolute value
Let's start by evaluating $|18-9|$:
$|18-9| = |9| = 9$

Step 2: Evaluate the outer absolute value
Now we substitute this result into the next layer:
$||18-9|+4| = |9+4| = |13| = 13$

Step 3: Rewrite the original inequality
Substituting our result back into the original inequality:
$|a| - ||18-9|+4| < 0$
$|a| - 13 < 0$

Step 4: Isolate the absolute value
Adding 13 to both sides:
$|a| < 13$

Step 5: Solve the absolute value inequality
The inequality $|a| < 13$ means that the distance from $a$ to 0 is less than 13. This is equivalent to:
$-13 < a < 13$

Conclusion: The solution to the inequality is $-13 < a < 13$, which matches choice 1.

Therefore, the necessarily true statement is $-13 < a < 13$.