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 $\text{ cm}$)

The region formed by the inequalities $2x + 3y - 5 \leq 0$,$4x - 3y + 2 \leq 0$,and $x \geq 0$ is:

To receive grade $A$ in a course,one must obtain an average of $90$ marks or more in five examinations (each of $100$ marks). If Sunita's marks in the first four examinations are $87, 92, 94,$ and $95,$ find the minimum marks that Sunita must obtain in the fifth examination to get grade $A$ in the course.

Solve $\frac{1 - |x|}{2 - |x|} \ge 0$.

Find all pairs of consecutive odd natural numbers,both of which are larger than $10$,such that their sum is less than $40$.

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