Answer
Please see the graph.
Work Step by Step
Blue line: $y\ge-x+2$
Orange line: $y\le2x+5$
To determine what sides of the lines to shade, we use a point not on the line. We can use (0,0) for the lines.
Blue line:
$y\ge-x+2$
$0\ge-1*0+2$
$0\ge 0+2$
$0\ge 2$ (false, so we shade the right side of the line)
Orange line:
$y\le2x+5$
$0\le2*0+5$
$0\le0+5$
$0\le 5$ (true, so we shade the right side of the line)
The solution area is the overlap of the two inequalities.
