Solve |b|-|12-3|+|5|<0: Multiple Absolute Value Inequality Challenge

These are known values that don't depend on the variable b. Evaluating them first simplifies your inequality from $|b|-|12-3|+|5|<0$ to the much easier $|b|-4<0$.

The absolute value inequality $|b| < 4$ means the distance from b to 0 is less than 4. This happens when b is between -4 and 4, so $-4 < b < 4$.

Then the solution would be $b < -4$ or $b > 4$. But in this problem, we have $|b| < 4$, which gives us the interval between -4 and 4.

Pick any value in your solution range, like b = 0. Substitute: $|0|-|12-3|+|5| = 0-9+5 = -4 < 0$ ✓. Try a value outside the range like b = 5: $|5|-9+5 = 1 > 0$, which doesn't satisfy the inequality.

Those ranges are either too wide or don't match our solution $|b| < 4$. For example, if $-10 < b < 10$ were correct, then b = 5 should work, but $|5|-4 = 1 > 0$, not < 0.