To simplify the expression $3x + 5x$, we will combine the like terms to obtain $8x$.

In algebra, simplifying an expression involves reducing it to its most basic form. When you encounter terms that are similar, known as “like terms,” you can combine them. Like terms are defined as terms that share the same variable raised to the same power. In the expression $3x + 5x$, both terms are like terms because they both include the variable $x$ raised to the first power.

To combine these like terms, you simply add their coefficients, which are the numerical values in front of the variables. In this case, the coefficients are $3$ and $5$. Adding these coefficients together gives us $3 + 5$, which equals $8$. Therefore, we can simplify $3x + 5x$ to $8x$.

Combining like terms is a fundamental skill in algebra, as it helps to simplify expressions and makes them easier to work with. This technique is particularly useful when solving equations or simplifying more complex algebraic expressions. It is important to remember that you can only combine terms that have the same variable with the same exponent. For instance, you cannot combine $3x$ and $5y$ because they represent different variables.