Solve 1331x-x^3+(11+x)(x^2-11x+121)geq0

$$1331x- { x }^{ 3 } +(11+x)( { x }^{ 2 } -11x+121) \geq 0$$

Solve for x

$$x\geq -1$$

Solution Steps

Use the distributive property to multiply 11+x by x^{2}-11x+121 and combine like terms.

$$1331x-x^{3}+1331+x^{3}\geq 0$$

Combine -x^{3} and x^{3} to get 0.

$$1331x+1331\geq 0$$

Subtract 1331 from both sides. Anything subtracted from zero gives its negation.

$$1331x\geq -1331$$

Divide both sides by 1331. Since 1331 is positive, the inequality direction remains the same.

$$x\geq \frac{-1331}{1331}$$

Divide -1331 by 1331 to get -1.

$$x\geq -1$$