What is (2x-1)*((-x+1)/2)<0 ?

The solution to (2x-1)*((-x+1)/2) 1

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(2x-1)*((-x+1)/2)<0

(2 x - 1) \cdot (\frac{- x + 1}{2}) < 0

x < \frac{1}{2} or x > 1

Solution steps

(2 x - 1) \frac{- x + 1}{2} < 0

Rewrite in standard form

- 2 x^{2} + 3 x - 1 < 0

Factor

- 2 x^{2} + 3 x - 1 : - (2 x - 1) (x - 1)

- (2 x - 1) (x - 1) < 0

Multiply both sides by

- 1

(reverse the inequality)

(- (2 x - 1) (x - 1)) (- 1) > 0 \cdot (- 1)

Simplify

(2 x - 1) (x - 1) > 0

Identify the intervals

x < \frac{1}{2} or x > 1

ln (\frac{5}{2})

8 x^{2} - 16 x + 6

3 x^{2} \geq 30

x^{2} - 11 x y - 60 y^{2}

- 0.5 x - 4 = 1.5

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