1. The problem asks to write down the two inequalities that define the shaded region on the graph. 2. From the description, the first boundary is a dashed diagonal line passing through points like (0,0), (1,1), (2,2), etc., which corresponds to the line $$y = x$$. 3. Since the shaded region is below this dashed line, the inequality is $$y < x$$. 4. The second boundary is a solid vertical line at $$x = 4$$. 5. The shaded region is to the left of this line, so the inequality is $$x \leq 4$$. 6. Therefore, the two inequalities defining the shaded region are: $$y < x$$ $$x \leq 4$$