The solution to 6x+27>x^2 is -3<x<9

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6x+27>x^2

Solution

6 x + 27 > x^{2}

- 3 < x < 9

Interval Notation

(- 3, 9)

Solution steps

6 x + 27 > x^{2}

Rewrite in standard form

6 x + 27 - x^{2} > 0

Factor

6 x + 27 - x^{2} : - (x + 3) (x - 9)

- (x + 3) (x - 9) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x + 3) (x - 9)) (- 1) < 0 \cdot (- 1)

Simplify

(x + 3) (x - 9) < 0

Identify the intervals

- 3 < x < 9

e^{0.3}

3 t^{2} - 108 a^{2}

5 x^{2} - 3 x - 5 = 3

2^{x + 1} + 2^{3 - x} \leq 8

7 x = 65.8