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

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

The value inside the absolute value brackets can be either positive or negative so (y - 9) must equal - 8 or --8 for \( \left|y - 9\right| \) to equal -8:

So, y = 17 or y = 1.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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 $1,200
i = 0.02 x $1,200
i = $24

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{6} \) ÷ \( \frac{4}{5} \) = \( \frac{1}{6} \) x \( \frac{5}{4} \)

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

\( \frac{1}{6} \) x \( \frac{5}{4} \) = \( \frac{1 x 5}{6 x 4} \) = \( \frac{5}{24} \) = \(\frac{5}{24}\)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: