We are asked to find the four inequalities that define the unshaded region R in the given XOY plane. The region is bounded by one oblique line and two horizontal and one vertical lines.

1. Problem Description

We are asked to find the four inequalities that define the unshaded region R in the given XOY plane. The region is bounded by one oblique line and two horizontal and one vertical lines.

2. Solution Steps

The region R is defined by four lines.

First, consider the oblique line. It intersects the y-axis at $y=2$. Its slope is $m = \frac{2-0}{0-(-2)} = \frac{2}{2} = 1$. The equation of this line is $y=x+2$. Since the unshaded region is above this line, the corresponding inequality is $y \ge x+2$.

Second, consider the upper horizontal line. It passes through $y=3$. Since the unshaded region is below the line, the inequality is $y \le 3$.

Third, consider the lower horizontal line. It passes through $y=-1$. Since the unshaded region is above the line, the inequality is $y \ge -1$.

Fourth, consider the vertical line. It passes through $x=2$. Since the unshaded region is to the left of this line, the inequality is $x \le 2$.

3. Final Answer

The four inequalities that define the unshaded region R are:

$y \ge x+2$

$y \le 3$

$y \ge -1$

$x \le 2$