The solution to 9x>x^2+14 is 2<x<7

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9x>x^2+14

Solution

9 x > x^{2} + 14

2 < x < 7

Interval Notation

(2, 7)

Solution steps

9 x > x^{2} + 14

Rewrite in standard form

9 x - 14 - x^{2} > 0

Factor

9 x - 14 - x^{2} : - (x - 2) (x - 7)

- (x - 2) (x - 7) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 2) (x - 7)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 2) (x - 7) < 0

Identify the intervals

2 < x < 7

- 16 x^{2} + 60 x + 16

\frac{( 76 + 74 + p )}{3} > 78

- x^{2} + 4 \geq 0

(7 - 2) (8 + 2)

n - 20 = - 26