The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

First, solve for \( \left|b - 6\right| \):

\( \left|b - 6\right| \) + 3 = -5
\( \left|b - 6\right| \) = -5 - 3
\( \left|b - 6\right| \) = -8

The value inside the absolute value brackets can be either positive or negative so (b - 6) must equal - 8 or --8 for \( \left|b - 6\right| \) to equal -8:

So, b = 14 or b = -2.

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

\( \frac{2}{6} \) x \( \frac{4}{5} \) = \( \frac{2 x 4}{6 x 5} \) = \( \frac{8}{30} \) = \(\frac{4}{15}\)

If the tiger has consumed 70 pounds of food in 5 days that's \( \frac{70}{5} \) = 14 pounds of food per day. The tiger needs to consume 154 - 70 = 84 more pounds of food to reach 154 pounds total. At 14 pounds of food per day that's \( \frac{84}{14} \) = 6 more days.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.