What is (5-x)*(2x-6)>0 ?

The solution to (5-x)*(2x-6)>0 is 3<x<5

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(5-x)*(2x-6)>0

(5 - x) \cdot (2 x - 6) > 0

3 < x < 5

Interval Notation

(3, 5)

Solution steps

(5 - x) (2 x - 6) > 0

Rewrite in standard form

- x^{2} + 8 x - 15 > 0

Factor

- x^{2} + 8 x - 15 : - (x - 3) (x - 5)

- (x - 3) (x - 5) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 3) (x - 5)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 3) (x - 5) < 0

Identify the intervals

3 < x < 5

2 x^{3} - 3 x^{2} + 7 x - 3 > 0

\frac{( x + 1 )}{( x - 1 ^{2} )} < - 1

\frac{( 3 x - 2 )}{( 9 x + 1 )} < \frac{1}{3}

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

x^{2} - 4 x - 7 < 0