solve for real x for the following inequality x(x-2)(x-5)/(x+3)^2(15-2x)^5 <0
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x( x -2)(x -5)/( x +3)²(15-2x)^5 < 0
equate given all terms to zero
x = 0
(x -2) = 0, => x = 2
(x -5) =0 => x = 5
(x +3) = 0 => x = -3
( 15 -2x ) =0 => x = 15/2
now use number line for solving this ,
see , above figure ,
answer , x €( -∞, -3)U ( -3, O) U( 2, 5) U ( 15/2 , ∞}
equate given all terms to zero
x = 0
(x -2) = 0, => x = 2
(x -5) =0 => x = 5
(x +3) = 0 => x = -3
( 15 -2x ) =0 => x = 15/2
now use number line for solving this ,
see , above figure ,
answer , x €( -∞, -3)U ( -3, O) U( 2, 5) U ( 15/2 , ∞}
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