What is (2x-6)(-2x+8)>0 ?

The solution to (2x-6)(-2x+8)>0 is 3<x<4

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(2x-6)(-2x+8)>0

(2 x - 6) (- 2 x + 8) > 0

3 < x < 4

Interval Notation

(3, 4)

Solution steps

(2 x - 6) (- 2 x + 8) > 0

Rewrite in standard form

- x^{2} + 7 x - 12 > 0

Factor

- x^{2} + 7 x - 12 : - (x - 3) (x - 4)

- (x - 3) (x - 4) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 3) (x - 4)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 3) (x - 4) < 0

Identify the intervals

3 < x < 4

\frac{( ( x - 5 ) ( x - 9 ) )}{( ( x - 3 ) ( x - 7 ) )} \leq 0

(x + 3) (2 x + 5) \leq (2 x + 1)^{2} + 6 x

2 x^{3} + 4 x^{2} - 13 x + 7 < 0

x^{3} \geq x^{2}

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