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SOLUTION: How do you know which test point to plug in to determine wether to shade up or down for the equation?
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Question 204777
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How do you know which test point to plug in to determine wether to shade up or down for the equation?
Answer by
RAY100(1637)
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To solve an inequality, first identify the line separating the regions.
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The line is solid if equalities (<= or >=) are involved,,,dashed if just inequalities(< or >).
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Now, to pick which side of the line is the "area of interest" we chose a test point. It can be any point in the region. Usually we pick one that makes for easy math,,like (0,0) or (1,1),,,,however any point will do, on either side of the line.
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Just substitute in the original inequality. If the resulting statement is true,,that side is the area of concern. If not, the other side is. (no need to pick another point on the other side of the line)
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for example,,,if y >= 2x+2,,let (0,0) be test point,,,result is 0>=2,,,This is not true, so area of concern is on the other side of the line.
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If we checked,,,(0,3),,,(which is on the other side of the line),
result is,,,,3>= 2,,,which is true, and now this side does define the area of concern.
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Please try it on several easy problem, until you have confidence.
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Have a good day