Question 123847
Example: 
3x - 4y < 2
1st: solve for "y":
y >= (3/4)x - (1/2)
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2nd: Graph the boundary which is y = (3/4)x-(1/2)
Graph this line as a dashed line because "equality" was not part of the equation.
{{{graph(400,300,-10,10,-10,10,(3/4)x-(1/2))}}}
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3rd: Select a test point that is not on the boundary, like (0,0)
4th: Check to see if this point satisfied the INEQUALITY y>(3/4)x-(1/2)
You get: 0 > (3/4)*0-(1/2) ; 0>-1/2
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Conclusion: That is true so the half-plane solution for the Inequality is on 
the same side of the boundary as the point (0,0).
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If the result had been false, the half-plane solution would be 
on the side that does not contain (0,0)
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Cheers,
Stan H.