First, solve for \( \left|b - 8\right| \):

\( \left|b - 8\right| \) - 9 = -8
\( \left|b - 8\right| \) = -8 + 9
\( \left|b - 8\right| \) = 1

The value inside the absolute value brackets can be either positive or negative so (b - 8) must equal + 1 or -1 for \( \left|b - 8\right| \) to equal 1:

So, b = 7 or b = 9.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (4 + 3) ÷ 3 x 5 - 5²
P: 5 + (7) ÷ 3 x 5 - 5²
E: 5 + 7 ÷ 3 x 5 - 25
MD: 5 + \( \frac{7}{3} \) x 5 - 25
MD: 5 + \( \frac{35}{3} \) - 25
AS: \( \frac{15}{3} \) + \( \frac{35}{3} \) - 25
AS: \( \frac{50}{3} \) - 25
AS: \( \frac{50 - 75}{3} \)
\( \frac{-25}{3} \)
-8\(\frac{1}{3}\)

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{60} \) = \( \frac{\frac{20}{20}}{\frac{60}{20}} \) = \( \frac{1}{3} \)

51% of the water consumption is industrial use and 32% is personal use so (51% - 32%) = 19% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{19}{100} \) x 50,000 gallons = 9,500 gallons.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.