SOLUTION: Linear and non-linear Inequalities For what values of x does the expression {{{ sqrt(( x )/(2-x)(5+x)) }}} represent a real number? Please solve this inequality drawing a number

Question 391771: Linear and non-linear Inequalities
For what values of x does the expression represent a real number?
Please solve this inequality drawing a number line and showing the interval notations.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
sqrt(( x )/(2-x)(5+x))
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The radicand must be positive.
Solve: (( x )/(2-x)(5+x))> 0
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Draw a number line and plot -5,0,2
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Test a value from each of the resulting intervals
in the inequality:
If x = -10 you get -/[+*-]>0; true so solutions in (-inf,-5)
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If x = -2 you get -/[+*+]>0; false
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If x = 1 you get +/[+*+]>0; true so solutions in (0,2)
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If x = 5 you get +/[-*+]>0; false
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Conclusion: (-inf,-5)U(0,2)
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Cheers,
Stan H.
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