1. The problem asks us to identify the variable in the expression $13x + 52$. 2. In algebra, a variable is a symbol that represents an unknown or changeable value. 3. The expression $13x + 52$ consists of three parts: the coefficient $13$, the variable $x$, and the constant $52$. 4. The coefficient is the number multiplying the variable, which is $13$ here. 5. The constant is a fixed number, which is $52$ here. 6. The variable is the letter that can change or vary, which is $x$ in this expression. 7. Therefore, the variable in the expression $13x + 52$ is $x$. Final answer: $x$