The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

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

\( \frac{5 x 5}{6 x 5} \) - \( \frac{6 x 3}{10 x 3} \)

\( \frac{25}{30} \) - \( \frac{18}{30} \)

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

\( \frac{25 - 18}{30} \) = \( \frac{7}{30} \) = \(\frac{7}{30}\)

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.

By buying two shirts, Roger will save $46 x \( \frac{10}{100} \) = \( \frac{$46 x 10}{100} \) = \( \frac{$460}{100} \) = $4.60 on the second shirt.

So, his total cost will be
$46.00 + ($46.00 - $4.60)
$46.00 + $41.40
$87.40

First, solve for \( \left|x + 5\right| \):

\( \left|x + 5\right| \) - 1 = -8
\( \left|x + 5\right| \) = -8 + 1
\( \left|x + 5\right| \) = -7

The value inside the absolute value brackets can be either positive or negative so (x + 5) must equal - 7 or --7 for \( \left|x + 5\right| \) to equal -7:

So, x = 2 or x = -12.