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Popular >

1/(x^3)>-27

Solution

\frac{1}{x ^{3}} > - 27

Solution

x < - \frac{1}{3} or x > 0

+2

Interval Notation

(- \infty, - \frac{1}{3}) \cup (0, \infty)

Decimal Notation

x < - 0.33333 \dots or x > 0

Solution steps

\frac{1}{x ^{3}} > - 27

Rewrite in standard form

\frac{1 + 27 x ^{3}}{x ^{3}} > 0

Factor

\frac{1 + 27 x ^{3}}{x ^{3}} : \frac{( 3 x + 1 ) ( 9 x ^{2} - 3 x + 1 )}{x ^{3}}

\frac{( 3 x + 1 ) ( 9 x ^{2} - 3 x + 1 )}{x ^{3}} > 0

Identify the intervals

x < - \frac{1}{3} or x > 0

Popular Examples

((2x-4))/((3-x))>= 1

\frac{( 2 x - 4 )}{( 3 - x )} \geq 1

(((x+2)(x^2-2x+1)))/((4+3x-x^2))>= 0

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

(x+1)/((x-1)^2)<1

\frac{x + 1}{( x - 1 ) ^{2}} < 1

((5-2x))/((3x^2-2x-16))<1

\frac{( 5 - 2 x )}{( 3 x ^{2} - 2 x - 16 )} < 1

(x^2-4x+4)(1-2x)(x^2+3x-1)x>0

(x^{2} - 4 x + 4) (1 - 2 x) (x^{2} + 3 x - 1) x > 0

Frequently Asked Questions (FAQ)

What is 1/(x^3)>-27 ?
The solution to 1/(x^3)>-27 is x<-1/3 \lor x>0