What is (x-1)^4*(x-3)^6*(x-2)^5*(x-4)^{10}>0 ?

The solution to (x-1)^4*(x-3)^6*(x-2)^5*(x-4)^{10}>0 is 2 4

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(x-1)^4(x-3)^6(x-2)^5*(x-4)^{10}>0

(x - 1)^{4} \cdot (x - 3)^{6} \cdot (x - 2)^{5} \cdot (x - 4)^{10} > 0

2 < x < 3 or 3 < x < 4 or x > 4

Interval Notation

(2, 3) \cup (3, 4) \cup (4, \infty)

Solution steps

(x - 1)^{4} (x - 3)^{6} (x - 2)^{5} (x - 4)^{10} > 0

Identify the intervals

2 < x < 3 or 3 < x < 4 or x > 4

\frac{1}{( x - 5 )} < 3

\frac{2}{( x - 1 )} \leq \frac{3}{( 2 x - 3 )}

(x - 1) (x - 5) (x - 15) \leq 0, (x - 3) (x - 10) > 0

[x + 6] > 4

\frac{( x + 5 ) ( x - 9 )}{( x - 12 )} > 0

What is (x-1)^4*(x-3)^6*(x-2)^5*(x-4)^{10}>0 ?
The solution to (x-1)^4*(x-3)^6*(x-2)^5*(x-4)^{10}>0 is 2<x<3\lor 3<x<4\lor x>4