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

\( \left|x - 5\right| \) + 6 = 2
\( \left|x - 5\right| \) = 2 - 6
\( \left|x - 5\right| \) = -4

The value inside the absolute value brackets can be either positive or negative so (x - 5) must equal - 4 or --4 for \( \left|x - 5\right| \) to equal -4:

So, x = 9 or x = 1.

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.

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

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

If the tiger has consumed 48 pounds of food in 6 days that's \( \frac{48}{6} \) = 8 pounds of food per day. The tiger needs to consume 72 - 48 = 24 more pounds of food to reach 72 pounds total. At 8 pounds of food per day that's \( \frac{24}{8} \) = 3 more days.