First, solve for \( \left|c - 5\right| \):

\( \left|c - 5\right| \) - 6 = 7
\( \left|c - 5\right| \) = 7 + 6
\( \left|c - 5\right| \) = 13

The value inside the absolute value brackets can be either positive or negative so (c - 5) must equal + 13 or -13 for \( \left|c - 5\right| \) to equal 13:

So, c = -8 or c = 18.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 20mph \times 3h \)
60 miles

To simplify a radical, factor out the perfect squares:

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