SOLUTION: Hello! And thank you for helping me with this question! Question: Find a solution to the inequality: x(7 -x)> 8 I tried distributing the x outside of the parenthesis to the

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Question 614317: Hello! And thank you for helping me with this question!
Question:
Find a solution to the inequality: x(7 -x)> 8
I tried distributing the x outside of the parenthesis to the 7 and -x in the parenthesis, but then I got stuck. Could you please help me solve this? Thank you!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find a solution to the inequality: x(7 -x)> 8
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7x - x^2 > 8
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x^2-7x+8 < 0
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Factor:
(x-8)(x+1) < 0
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Draw a number line:
Plot the points x = -1 and x = 8
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Test a value from each of the 3 intervals to see where
the solutions are for the inequality.
Let x = -10 ; you get -*- < 0 ; false
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Let x = 0 ; you get -*+ < 0 ; true. So solutions in -1< x < 8
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Let x = 10 ; you get +*+ < 0 ; false.
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Solutions are in the interval (-1,8)
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Cheers,
Stan H.