Solve the following inequality: $|x-1|+|x-2|+|x-3| \geq 6$

The region represented by the inequations $2x + 3y \leqslant 18$,$x + y \geqslant 10$,$x \geqslant 0$,$y \geqslant 0$ is

Find all pairs of consecutive odd positive integers,both of which are smaller than $10$,such that their sum is more than $11$.

Let $2\sin^2 x + 3\sin x - 2 > 0$ and $x^2 - x - 2 < 0$ ($x$ is measured in radians). Then $x$ lies in the interval

The common region of the solution of the inequations $x+y \geq 5$,$y \leq 4$,$x \geq 2$,$x, y \geq 0$ is

In a manufacturing company,the cost and revenue functions of a product are given by $C(x) = 500 + \frac{5}{2}x$ and $R(x) = 3x$,where $x$ is the number of items produced and sold. How many items must be sold to realize no profit or loss? Is there any profit?