Solve the inequality x/2 ≥ 1+4/x and express the solution in terms of intervals.
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justaguide
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We have to solve the inequation x/2 >= 1 + 4/x
x/2 >= 1 + 4/x
=> x >= 2 + 8/x
If we assume that x >=0, we can multiply both the sides of the inequation with x without changing the sign.
=> x^2 >= 2x + 8
=> x^2 - 2x - 8 >= 0
=> x^2 - 4x + 2x - 8 >= 0
=> x( x - 4) + 2(x - 4) >=0
=> (x - 4)(x + 2) >= 0
For (x - 4)(x + 2) >= 0 both (x - 4)...
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