Sure, let's work through the problem to determine which expression is a monomial.
A monomial is an algebraic expression consisting of only one term. This term consists of a product of constants and variables raised to non-negative integer powers. Here's the step-by-step analysis for each given option:
1. \(\frac{1}{x}\):
- This expression can be rewritten as \(x^{-1}\), where the variable \(x\) is raised to the power of \(-1\).
- Since \(-1\) is not a non-negative integer, \(\frac{1}{x}\) is not a monomial.
2. \(3 x^{0.5}\):
- In this expression, \(x\) is raised to the power of \(0.5\).
- The power \(0.5\) is not an integer, so \(3 x^{0.5}\) is not a monomial.
3. \(x + 1\):
- This expression consists of two terms: \(x\) and \(1\).
- Since a monomial can only have one term, \(x + 1\) is not a monomial. It is actually a binomial.
4. \(7\):
- This is a constant term, where no variable is present.
- A constant is considered a monomial since it can be thought of as \(7x^0\), where the variable \(x\) is raised to the power of \(0\) (and \(0\) is a non-negative integer).
Therefore, the expression that is a monomial is:
[tex]\[ \boxed{7} \][/tex]
