Question

The inequality $x^4+1<-5$has no solution. Explain why.

Short answer

Because $x^4+1$is always positive.

Hence, the given inequality has no solutions.

Step-by-step solution

Given information

The given inequality is$x^4+1<-5$

Determine the solution of the given inequality,

$x^4$always satisfies the inequality $x^4\ge 0$.

Example: $-1·-1·-1·-1=1$

So, $x^4+1\ge 0$.

Write the conclusion

$x^4+1\ge 0$ is always positive