1. The problem asks for the two double inequalities that define the shaded rectangular region on the coordinate plane. 2. The region is bounded by vertical lines at $x = -4$ (dashed) and $x = 3$ (solid), and horizontal lines at $y = 1$ (solid) and $y = 6$ (dashed). 3. A dashed boundary means the inequality is strict (does not include the boundary), while a solid boundary means the inequality is inclusive (includes the boundary). 4. For the vertical boundaries: - Left boundary at $x = -4$ is dashed, so $x > -4$. - Right boundary at $x = 3$ is solid, so $x \leq 3$. 5. For the horizontal boundaries: - Bottom boundary at $y = 1$ is solid, so $y \geq 1$. - Top boundary at $y = 6$ is dashed, so $y < 6$. 6. Combining these, the double inequalities defining the shaded region are: $$-4 < x \leq 3$$ $$1 \leq y < 6$$ These inequalities describe all points $(x,y)$ inside the shaded rectangle, including the solid boundaries but excluding the dashed ones.