First, solve for \( \left|y - 4\right| \):

\( \left|y - 4\right| \) + 5 = -8
\( \left|y - 4\right| \) = -8 - 5
\( \left|y - 4\right| \) = -13

The value inside the absolute value brackets can be either positive or negative so (y - 4) must equal - 13 or --13 for \( \left|y - 4\right| \) to equal -13:

So, y = 17 or y = -9.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

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

\( \frac{6 x 3}{3 x 3} \) - \( \frac{8 x 1}{9 x 1} \)

\( \frac{18}{9} \) - \( \frac{8}{9} \)

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

\( \frac{18 - 8}{9} \) = \( \frac{10}{9} \) = 1\(\frac{1}{9}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.