SOLUTION: I'm attempting to help my child with an absolute value problem that she cannot solve and it has been a long time since I have had Algebra. Help please! Please show work with expl
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Question 147379: I'm attempting to help my child with an absolute value problem that she cannot solve and it has been a long time since I have had Algebra. Help please! Please show work with explanation and then I will work it through with her not providing the answer directly. Thanks!
Find the absolute value inequality for the following:
x < 6 or x > 11 Found 2 solutions by stanbon, nabla:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! I'm attempting to help my child with an absolute value problem that she cannot solve and it has been a long time since I have had Algebra. Help please! Please show work with explanation and then I will work it through with her not providing the answer directly. Thanks!
Find the absolute value inequality for the following:
x < 6 or x > 11
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Draw a number line; mark 6 and 11 on the line.
Find the point half-way between 6 and 11: that is 8.5 or 8 1/2
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x < 6 and x>11 are all the points that are more than 2.5 away
from that middle point.
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The Absolute Inequality must describe all the points that are
more than 2.5 units from 8.5:
|x-8.5| > 2.5
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Cheers,
Stan H.
You can put this solution on YOUR website! Essentially what we want here is
x < 6 or x > 11
Look at the endpoints. 6 and 11 are 5 units apart. Half of 5 is 2.5. So you want to adjust the inequality so it relates to –2.5 and 2.5 INSTEAD of 6 and 11. You will need to subtract 8.5 all around.
x-8.5 < 6-8.5 or x-8.5 > 11-8.5
x-8.5 < -2.5 or x-8.5 > 2.5
Now, recall GOLA. This is a simple rule that says if the absolute valued terms are greater, we will use OR. If the absolute valued terms are less, we will use and.
Since this is the "greater than" format (use of or), the absolute-value inequality will be of the form "absolute value of something is greater than 2.5". You can convert this nicely to
|x-8.5| > 2.5
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