What is -x^2+1>4x+1 ?

The solution to -x^2+1>4x+1 is -4<x<0

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-x^2+1>4x+1

- x^{2} + 1 > 4 x + 1

- 4 < x < 0

Interval Notation

(- 4, 0)

Solution steps

- x^{2} + 1 > 4 x + 1

Rewrite in standard form

- x^{2} - 4 x > 0

Factor

- x^{2} - 4 x : - x (x + 4)

- x (x + 4) > 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

x (x + 4) < 0

Identify the intervals

- 4 < x < 0

5 x^{2} + 30 x + 125 = 0

- 3 + 39 \geq 7 m + 5 m

- k + 78 = 98 - 20

2 - x < x

4 t = 12 - 4 t