If  is a real number, the inequality 4 + 5 < 0 is satisfied for:A. all B.  = −5C. no values of D.  > −5E.  < − 4p5

Break Down the Problem

1. We need to analyze the inequality $x^4 + 5 < 0$.
2. Determine the feasible values of $x$ that can satisfy the inequality.

Relevant Concepts

1. Understanding the Function: The function $x^4$ is always non-negative for all real numbers $x$, because the fourth power of any real number is either zero or positive.
2. Constant Term: The constant term in this inequality is $+5$, which is also positive.

Analysis and Detail

1. The expression $x^4 + 5$ will always yield a value greater than or equal to 5 for any real $x$ because: $x^4 \geq 0 \Rightarrow x^4 + 5 \geq 0 + 5 = 5$
2. Therefore, $x^4 + 5$ can never be less than 0.

Verify and Summarize

1. Since $x^4 + 5$ is always greater than or equal to 5, there are no values of $x$ that can satisfy the inequality $x^4 + 5 < 0$.

Final Answer

C. no values of $x$