If the point $(a, a)$ is placed between the lines $|x + y| = 4$,then

Find the set of all values of $x$ satisfying $\frac{x^4 - 4x^3 + 3x^2}{(x^2 - 4)(x^2 - 7x + 10)} \ge 0$.

$A$ 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?

$A$ solution is to be kept between $68\,^{\circ} F$ and $77\,^{\circ} F$. What is the range in temperature in degree Celsius $(C)$ if the Celsius/Fahrenheit $(F)$ conversion formula is given by $F = \frac{9}{5} C + 32$?

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}$ is equal to

The longest side of a triangle is twice the shortest side and the third side is $3 \text{ cm}$ more than the shortest side. If the perimeter of the triangle is at least $51 \text{ cm}$, find the minimum length of the shortest side. (in $\text{ cm}$)