Answer:
[tex]y>4-x[/tex]
Step-by-step explanation:
First, see at dotted line. This line passes through the points (4,0) and (0,4). Then the equation of this line is
[tex]\dfrac{x-4}{0-4}=\dfrac{y-0}{4-0}\\ \\\dfrac{x-4}{-4}=\dfrac{y}{4}\\ \\x-4=-y\\ \\y=4-x[/tex]
This line divides the coordinate plane into two regions where [tex]y<4-x[/tex] and [tex]y>4-x[/tex]. The origin does not belong to the shaded region, so its coordinates does not satisfy the inequality. Check
[tex]0<4-0\\ \\0<4,[/tex]
then the origin belongs to the region with inequality [tex]y<4-x.[/tex]
Then the needed inequality is [tex]y>4-x.[/tex]
Note that sign is without notion "or equal to", because the line is dotted.
