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Question 84787: I have real troubles with these. Please help.
Graph the inequality.
y is greater than or equal to 3x
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Solve this by graphing the line y = 3x.
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This line represents the points in which y = 3x. The points above this line are all the
points in which y is greater than 3x. You can identify these points by shading in the area
above the graphed line, and include the graphed line in the shading. Then you can say that
any point within the shaded area has a y value that will be greater than 3 times its
corresponding x value.
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To help you visualize this, here's a picture of the graph y = 3x
.
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Imagine that starting on the line and going upward you shade the entire area above the
line.
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Then if you put your pencil point on any place in the shaded area, the y value of that
point will be equal to or greater than 3 times its x value. For example, find the point
(-3, +1). That point is above the line. It has an x value of -3 and a y value of +1. For
that point 3 times x is -9. And you can see that with a value of +1 y is greater than the
3x value of -9. [+1 is greater than -9 by definition. A positive number is greater than
a negative number.] Another example, locate the point (1, 6). It also is in the shaded area
above the line. 3 times the x value of 1 is 3 and the y value of 6 is greater than 3. So
the point (1, 6) is in the solution set.
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On the other hand, if you put your pencil point any place in the unshaded area below the
line, the y value of that point will be less that 3 times its corresponding x value.
As an example of this, find the point ( 2, 1). It is in the unshaded area below the graphed
line. Three times the x value of this point is 3*2 or 6. It is greater than the y value
of 1. For this point it is not true that y is greater than or equal to 3x because 1
is not greater than or equal to 6. So this point is not in the solution set to this problem.
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Hopefully this will make some sense and eventually you'll see the concept.
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