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

\( \left|y - 9\right| \) - 8 = -6
\( \left|y - 9\right| \) = -6 + 8
\( \left|y - 9\right| \) = 2

The value inside the absolute value brackets can be either positive or negative so (y - 9) must equal + 2 or -2 for \( \left|y - 9\right| \) to equal 2:

So, y = 7 or y = 11.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{9 x 2}{8 x 2} \) + \( \frac{4 x 1}{16 x 1} \)

\( \frac{18}{16} \) + \( \frac{4}{16} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{18 + 4}{16} \) = \( \frac{22}{16} \) = 1\(\frac{3}{8}\)

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

The amount of flour you need is (2\(\frac{5}{8}\) - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{21}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{15}{8} \) cups
1\(\frac{7}{8}\) cups

The factors of 44 are [1, 2, 4, 11, 22, 44] and the factors of 28 are [1, 2, 4, 7, 14, 28]. They share 3 factors [1, 2, 4] making 4 the greatest factor 44 and 28 have in common.