A related function is graphed Solve the given inequality 8xx

A related function is graphed. Solve the given inequality. 8x/x^2 - 16 greaterthanorequalto 0 The solution is. (Type your answer in interval notation.)

Solution

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Kindly note that for the given inequality to be true , both numerator and denominator has to be greater than 0.

Now for numerator > 0, all values of x has to be greater than or equal to 0.

i.e. x belongs to [0, Infinity)...................................................(1)

Secondly for denominator to be greater than equal to 0 i.e.

x^2 - 16 > 0 ie.

x belongs to (-Infinity,-4] U [4, Infinity)..............................................(2)

From (1) and (2) it can be deduced that for complete expression to be greater than equal to 0,

x belongs to [4,Infinity)

Solution