What is x*(x+2)^2*(x-1)^5*(2x-3)*(x-3)^4>= 0 ?

The solution to x*(x+2)^2*(x-1)^5*(2x-3)*(x-3)^4>= 0 is x=-2\lor 0 = 3/2

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x(x+2)^2(x-1)^5(2x-3)(x-3)^4>= 0

x \cdot (x + 2)^{2} \cdot (x - 1)^{5} \cdot (2 x - 3) \cdot (x - 3)^{4} \geq 0

x = - 2 or 0 \leq x \leq 1 or x \geq \frac{3}{2}

Interval Notation

x = - 2 \cup [0, 1] \cup [\frac{3}{2}, \infty)

Decimal Notation

x = - 2 or 0 \leq x \leq 1 or x \geq 1.5

Solution steps

x (x + 2)^{2} (x - 1)^{5} (2 x - 3) (x - 3)^{4} \geq 0

Identify the intervals

x = - 2 or 0 \leq x \leq 1 or x \geq \frac{3}{2}

\frac{( x ^{2} - 2 x ) ( 2 x - 2 ) - 9 \cdot ( 2 x - 2 )}{( x ^{2} - 2 x )} \leq 0

\frac{( ( 2 x + 1 ) ( x + 4 ) )}{( x ^{2} )} \geq 0

(x^{2} - 16) \cdot (x^{2} - 4) < 0

(x - 2) (x - 2) - 15 < x - 2 + x - 2

3 x^{2} - 4 < 5

What is x*(x+2)^2*(x-1)^5*(2x-3)*(x-3)^4>= 0 ?
The solution to x*(x+2)^2*(x-1)^5*(2x-3)*(x-3)^4>= 0 is x=-2\lor 0<= x<= 1\lor x>= 3/2