Solve |d|-|13-8|+|3|<0: Multiple Absolute Value Inequality

These are constants that you can calculate immediately! $|13-8| = |5| = 5$ and $|3| = 3$. Simplifying these makes your inequality much easier to work with.

The absolute value inequality $|d| < 2$ means the distance from d to zero is less than 2. This gives us $-2 < d < 2$.

Double-check your arithmetic! We have $|d| - 5 + 3 < 0$, which simplifies to $|d| - 2 < 0$, so $|d| < 2$.

Pick a test value like d = 0: $|0| - |13-8| + |3| = 0 - 5 + 3 = -2 < 0$ ✓. Try d = 3: $|3| - 5 + 3 = 1 > 0$ ✗, confirming d = 3 is outside our solution.

That would be the solution to $|d| < 6$, not $|d| < 2$. Always double-check your final simplified inequality before writing the solution!