First, solve for \( \left|b - 1\right| \):

\( \left|b - 1\right| \) + 7 = -2
\( \left|b - 1\right| \) = -2 - 7
\( \left|b - 1\right| \) = -9

The value inside the absolute value brackets can be either positive or negative so (b - 1) must equal - 9 or --9 for \( \left|b - 1\right| \) to equal -9:

So, b = 10 or b = -8.

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $200
i = 0.04 x $200

No payments were made so the total amount due is the original amount + the accumulated interest:

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

6x⁶ x 4x⁶
(6 x 4)x^{(6 + 6)}
24x¹²

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{405mi}{45mph} \)
9 hours

50% of the water consumption is industrial use and 28% is personal use so (50% - 28%) = 22% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{22}{100} \) x 50,000 gallons = 11,000 gallons.