Question 1046917: Solve the inequalities by graphing
y<=4x-1
y>3x-1
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 
You find which side the inequality holds by setting x and y equal to 0. If the inequality is true, that entire side of the line that contains the origin is true..
For the first graph, the one tilted less from the vertical (steeper), it is the area below or to the right of that line. At the origin, 0<=-1, and that is not true, so the other side of the line has the inequality work.
For the second graph, less steep, at the origin, 0>-1, and that is true, so the side of the line containing the origin is true.
Where both halves overlap, the inequality is solved. That would be to the left of the green line and to the right of the red line, or where x>0.
That occurs in the thin strip that begins at (0,-1). The point itself is not part of the overlap, because y>3x-1, not greater than or equal to.
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For any positive x, this works. x=1/2 and y<=1, and y >0.5
For x=3, y<=11 and y>8
Negative x should not work.
Pick x=-1/2
y<=-3
y>-2.5 There is no solution here
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