To multiply terms with radicals, multiply the coefficients and radicands separately:

8\( \sqrt{8} \) x 4\( \sqrt{2} \)
(8 x 4)\( \sqrt{8 \times 2} \)
32\( \sqrt{16} \)

Now we need to simplify the radical:

32\( \sqrt{16} \)
32\( \sqrt{4^2} \)
(32)(4)
128

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

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).

To add 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 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{9 x 5}{3 x 5} \) + \( \frac{9 x 3}{5 x 3} \)

\( \frac{45}{15} \) + \( \frac{27}{15} \)

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

\( \frac{45 + 27}{15} \) = \( \frac{72}{15} \) = 4\(\frac{4}{5}\)

First, solve for \( \left|c + 9\right| \):

\( \left|c + 9\right| \) + 0 = 1
\( \left|c + 9\right| \) = 1 + 0
\( \left|c + 9\right| \) = 1

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

So, c = -10 or c = -8.