Answer:
The right answer is the third:
[tex]\left \{ {{y\leq x+3} \atop {y<-x-4}} \right.[/tex]
Step-by-step explanation:
The continuous line is the graph of the function y=x+3.
If we check a any point in the colored area, the inequality must be true.
For example: Point(-5;-5)
We replace the values in the inequality:
y≤x+3
-5 ≤ -5 + 3
-5 ≤ -2
The point fatisfies the inequality.
Secondly, the non-continuous line is the graph of the function y= -x - 4
The line is dotted because the points in the line y= -x - 4 are not included by the inequality.
We check the same point in the colored area.
Point(-5;-5)
y <-x-4
-5 < -(-5) - 4
-5 < 5 - 4
-5 < 1
The point satisfies the inequality, so the point of the area is included by the inequality.
