If the tiger has consumed 45 pounds of food in 5 days that's \( \frac{45}{5} \) = 9 pounds of food per day. The tiger needs to consume 108 - 45 = 63 more pounds of food to reach 108 pounds total. At 9 pounds of food per day that's \( \frac{63}{9} \) = 7 more days.

First, solve for \( \left|x - 7\right| \):

\( \left|x - 7\right| \) - 5 = -2
\( \left|x - 7\right| \) = -2 + 5
\( \left|x - 7\right| \) = 3

The value inside the absolute value brackets can be either positive or negative so (x - 7) must equal + 3 or -3 for \( \left|x - 7\right| \) to equal 3:

So, x = 4 or x = 10.

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

\( \frac{4}{8} \) x \( \frac{2}{7} \) = \( \frac{4 x 2}{8 x 7} \) = \( \frac{8}{56} \) = \(\frac{1}{7}\)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-3a⁶ + 6a⁶
(-3 + 6)a⁶
3a⁶

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.