1. The problem asks for the two double inequalities that define the shaded rectangular region bounded by vertical lines at $x=-3$ (dashed) and $x=2$ (solid), and horizontal lines at $y=1$ (solid) and $y=5$ (dashed). 2. For vertical boundaries, the region lies between $x=-3$ and $x=2$. Since the line at $x=-3$ is dashed, the inequality is strict: $x > -3$. The line at $x=2$ is solid, so the inequality includes equality: $x \leq 2$. 3. For horizontal boundaries, the region lies between $y=1$ and $y=5$. The line at $y=1$ is solid, so $y \geq 1$. The line at $y=5$ is dashed, so $y < 5$. 4. Combining these, the two double inequalities defining the shaded region are: $$-3 < x \leq 2$$ $$1 \leq y < 5$$ These inequalities describe all points $(x,y)$ inside the rectangle, including the solid boundary lines but excluding the dashed ones.