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 $\text{ cm}$)

Solve the following system of inequalities: $\frac{2x+1}{7x-1} > 5$ and $\frac{x+7}{x-8} > 2$.

The longest side of a triangle is $3$ times the shortest side and the third side is $2 \, cm$ shorter than the longest side. If the perimeter of the triangle is at least $61 \, cm$,find the minimum length of the shortest side. (in $, cm$)

The set of all real values of $x$ satisfying the inequation $\frac{8x^2-14x-9}{3x^2-7x-6} > 2$ is

If $\theta$ is an acute angle and $\sin\theta = \frac{p - 6}{8 - p}$, then $p$ must satisfy:

$A$ man wants to cut three lengths from a single piece of board of length $91 \, cm$. The second length is to be $3 \, cm$ longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least $5 \, cm$ longer than the second?