What is -x^2+1>3x+1 ?

The solution to -x^2+1>3x+1 is -3<x<0

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-x^2+1>3x+1

- x^{2} + 1 > 3 x + 1

- 3 < x < 0

Interval Notation

(- 3, 0)

Solution steps

- x^{2} + 1 > 3 x + 1

Rewrite in standard form

- x^{2} - 3 x > 0

Factor

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

- x (x + 3) > 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

x (x + 3) < 0

Identify the intervals

- 3 < x < 0

3 x + 5 \leq - 7

12 a^{3} + 2 a^{2} - 192 a - 32

3 x^{2} - 3 x

k^{2} + 6 = 6

(x - 4) (x - 2)^{2} > 0