Answer :
To determine which expression is a monomial, we need to first understand what defines a monomial. A monomial is an algebraic expression that consists of only one term. The term can be a constant, a variable raised to a non-negative integer power, or a product of such variables and constants.
Let's analyze the given expressions to see which one fits the definition of a monomial:
1. \(\frac{1}{x}\): This expression is not a monomial because it contains a variable in the denominator. Monomials cannot have variables in the denominator; their exponents must be non-negative integers.
2. \(3 x^{0.5}\): This expression is not a monomial because the exponent of \(x\) is \(0.5\), which is not a non-negative integer. Monomials must have exponents that are whole numbers (0, 1, 2, etc.).
3. \(x + 1\): This expression is not a monomial because it consists of two separate terms (\(x\) and 1). A monomial must consist of only one term.
4. 7: This expression is a monomial because it is a single constant term. The exponent here is implicitly zero (since \(7 = 7x^0\)), which is a non-negative integer.
Given our analysis, the only expression that is a monomial is 7. So, the correct answer is:
[tex]\[ \boxed{7} \][/tex]
Let's analyze the given expressions to see which one fits the definition of a monomial:
1. \(\frac{1}{x}\): This expression is not a monomial because it contains a variable in the denominator. Monomials cannot have variables in the denominator; their exponents must be non-negative integers.
2. \(3 x^{0.5}\): This expression is not a monomial because the exponent of \(x\) is \(0.5\), which is not a non-negative integer. Monomials must have exponents that are whole numbers (0, 1, 2, etc.).
3. \(x + 1\): This expression is not a monomial because it consists of two separate terms (\(x\) and 1). A monomial must consist of only one term.
4. 7: This expression is a monomial because it is a single constant term. The exponent here is implicitly zero (since \(7 = 7x^0\)), which is a non-negative integer.
Given our analysis, the only expression that is a monomial is 7. So, the correct answer is:
[tex]\[ \boxed{7} \][/tex]
