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I don't get how you would know which way to shade the inequality when it's true or false.

For example the inequality 2x+3y> 12
When I solve it it's y>-2/3x+4

But when I graph the line how would I know which side to shade?

  • Algebra -

    2x + 3y > 12.

    Graph 2x + 3y = 12.
    Use the following points:
    (0,4), (6,0).
    The graph should be a dotted line,
    because the boundary line(graph) is not
    a part of the solution. Therefore, the
    points on the graph should not satisfy
    the inequality. Let's test the 1st point:
    2*0 + 3*4 > 12
    12 > 12. Not true.

    Imagine that the graph is a ramp and you are walking UP the ramp. The solution is to your right because the
    arrow(>) points to the right. This is true only when the inequality is in the
    standard form as given. Also, you must be walking UP the ramp.

    The following points are to the rt. as
    you walk UP the ramp and should,therefore,satisfy the inequality:

    (0,5), (7,0).
    2*0 + 3*5 > 12
    15 > 12. True.

    Test the 2nd point.

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