First, solve for \( \left|b - 9\right| \):

\( \left|b - 9\right| \) + 8 = 3
\( \left|b - 9\right| \) = 3 - 8
\( \left|b - 9\right| \) = -5

The value inside the absolute value brackets can be either positive or negative so (b - 9) must equal - 5 or --5 for \( \left|b - 9\right| \) to equal -5:

So, b = 14 or b = 4.

The greatest common factor (GCF) is the greatest factor that divides two integers.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{5} \) x \( \frac{1}{5} \) = \( \frac{1 x 1}{5 x 5} \) = \( \frac{1}{25} \) = \(\frac{1}{25}\)

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

There are 3 4-passenger taxis available so that's 3 x 4 = 12 total seats. There are 16 people needing transportation leaving 16 - 12 = 4 who will have to find other transportation.