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

To solve this problem, we'll follow these steps:

• Step 1: Simplify the constants in the inequality.

• Step 2: Rearrange the inequality into a solvable form.

• Step 3: Analyze the resulting inequality to find the acceptable range of $d$.

Now, let's work through each step:
Step 1: Calculate the absolute values:
- $|13 - 8| = |5| = 5$
- $|3| = 3$

So the inequality becomes:
|d| - 5 + 3 < 0

Simplify the constants:
|d| - 2 < 0

Step 2: Rearrange by isolating $|d|$:
|d| < 2

Step 3: Solve |d| < 2 :
The expression |d| < 2 results in the inequality -2 < d < 2 .