SOLUTION: How do you solve and/or graph inequalities?

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Question 124603: How do you solve and/or graph inequalities?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve and/or graph inequalities?
Let's say you have 3y + 6x <= 12 and you want to graph the solution:
1st: solve for "y"
y <= -2x+4
2nd: Graph the equality which is the boundary of the inequality:
y = -2x+4
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C-2x%2B4%29
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3rd: Determine what side of the line is the solution for the
inequality.
How:
Take a test point that is not on the boundary, like (0,0)
Substitute those x/y values into the inequality to see if
you get a true statement:
0 < -2*0 +4: This is true so the side with (0,0) is
the solution set; Shade it.
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The full solution is the boundary line plus the half-plane
that contains (0,0).
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If "equality" was not part of the problem, the boundary line
should be drawn as a dashed line as it is not part of the
solution. The test point would still reveal which side of
the dashed line is the solution for the inequality.
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Cheers,
Stan H.