What is (1-0.25*x)*(20+x)>20 ?

The solution to (1-0.25*x)*(20+x)>20 is -16<x<0

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(1-0.25x)(20+x)>20

(1 - 0.25 \cdot x) \cdot (20 + x) > 20

- 16 < x < 0

Interval Notation

(- 16, 0)

Solution steps

(1 - 0.25 x) (20 + x) > 20

Rewrite in standard form

- 0.25 x^{2} - 4 x > 0

Factor

- 0.25 x^{2} - 4 x : - x (0.25 x + 4)

- x (0.25 x + 4) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (0.25 x + 4)) (- 1) < 0 \cdot (- 1)

Simplify

x (0.25 x + 4) < 0

Identify the intervals

- 16 < x < 0

x^{2} - x + 1 \geq 0

\frac{3}{2 x - 1} < - 2

x (x - 10) < - 2 x - 7

\frac{( x + 3 )}{( x + 1 )} < 5

x \cdot (x + 2)^{2} \cdot (x - 1)^{5} \cdot (2 x - 3) \cdot (x - 3)^{4} \geq 0