To subtract these radicals together their radicands must be the same:

5\( \sqrt{18} \) - 9\( \sqrt{2} \)
5\( \sqrt{9 \times 2} \) - 9\( \sqrt{2} \)
5\( \sqrt{3^2 \times 2} \) - 9\( \sqrt{2} \)
(5)(3)\( \sqrt{2} \) - 9\( \sqrt{2} \)
15\( \sqrt{2} \) - 9\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

First, solve for \( \left|x + 8\right| \):

\( \left|x + 8\right| \) - 1 = -5
\( \left|x + 8\right| \) = -5 + 1
\( \left|x + 8\right| \) = -4

The value inside the absolute value brackets can be either positive or negative so (x + 8) must equal - 4 or --4 for \( \left|x + 8\right| \) to equal -4:

So, x = -4 or x = -12.

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

\( \frac{2}{8} \) x \( \frac{4}{9} \) = \( \frac{2 x 4}{8 x 9} \) = \( \frac{8}{72} \) = \(\frac{1}{9}\)

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 area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 6 meters so the equation becomes: 2w + 2h = 6.

Putting these two equations together and solving for width (w):

2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²