Answer
Please see the graph.
Work Step by Step
Red line: $3x-2y\le4$
Blue line: $2x+y\ge5$
Green line: $y\le4$
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.
Red line:
$3x-2y\le4$
$3*0-2*0\le4$
$0-0\le4$
$0\le4$ (true, so we shade to the left of the line)
Blue line:
$2x+y\ge5$
$2*0+0\ge5$
$0+0 \ge 5$
$0 \ge 5$ (false, so we shade the right side of the line)
Green line:
$y\le4$
$0\le4$ (true, so we shade below the line)
The solution area is the overlap of the three inequalities.
