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

Question

Given:

$|b|-|12-3|+|5|<0$

Which of the following statements is necessarily true?

We have the inequality:

$|b|-|12-3|+|5|<0$

First, evaluate the known absolute values:

Substitute these into the inequality:

$|b| - 9 + 5 < 0$

Which simplifies to:

$|b| - 4 < 0$

Adding 4 to both sides gives:

$|b| < 4$

The inequality $|b| < 4$ means that $b$ must be in the range:

$-4 < b < 4$

Thus, the correct choice for the solution is: $-4 < b < 4$ .

$-4 < b < 4$