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

The origin belongs to a region between the lines $x+2y-5=0$ and $3x-4y+5=0$. The number of points in that region of the form $((\alpha-1)^2, \alpha)$,where $\alpha \in \mathbb{Z}$,is

Solve the following system of inequalities: $\frac{x}{2x+1} \geq \frac{1}{4}$ and $\frac{6x}{4x-1} < \frac{1}{2}$.

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

Let $m, n$ be real numbers such that $0 \leq m \leq \sqrt{3}$ and $-\sqrt{3} \leq n \leq 0$. The minimum possible area of the region of the plane consisting of points $(x, y)$ satisfying the inequalities $y \geq 0$,$y - 3 \leq mx$,and $y - 3 \leq nx$ is

Solve the following inequality: $\frac{|x-1|}{x+2} < 1$.