The constraints $x+y \leq 4$,$3x+3y \geq 18$,$x \geq 0$,$y \geq 0$ define:

The maximum value of $x$ in the set $\{x \in R : \sqrt{x+2} > \sqrt{8-x^2}\}$ is:

In drilling the world's deepest hole,it was found that the temperature $T$ in degrees Celsius,$x \text{ km}$ below the earth's surface,is given by $T = 30 + 25(x - 3)$,where $3 \leq x \leq 15$. At what depth will the temperature be between $155^{\circ}C$ and $205^{\circ}C$?

Solve for $x$ in the following inequality: $\frac{4}{x+1} \leq 3 \leq \frac{6}{x+1}$ where $x > 0$.

$A$ company manufactures cassettes. Its cost and revenue functions are $C(x) = 26000 + 30x$ and $R(x) = 43x$,respectively,where $x$ is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

Find the sum of all integral values of $a$ such that the equation $||x - 2| - |3 - x|| = 2 - a$ has a solution.