First, solve for \( \left|x + 2\right| \):

\( \left|x + 2\right| \) - 1 = 2
\( \left|x + 2\right| \) = 2 + 1
\( \left|x + 2\right| \) = 3

The value inside the absolute value brackets can be either positive or negative so (x + 2) must equal + 3 or -3 for \( \left|x + 2\right| \) to equal 3:

So, x = -5 or x = 1.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

3y⁶ x 2y⁶
(3 x 2)y^{(6 + 6)}
6y¹²

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

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.

If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 40 large cakes are needed for the party so \( \frac{40}{12} \) = 3\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 14 x 4 = 56 small cakes during that time. 460 small cakes are needed for the party so \( \frac{460}{56} \) = 8\(\frac{3}{14}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 9 = 13 cooks.