The term expressions keeps coming up in Algebra. It's kind of an important distinction. We have operators, constants, and variables that we put together to form expressions. If we set that expression equal to something, we call than an equation.
3x + 16 is an expression. If I asked you to solve that for x, my request would be meaningless because you don't solve an expression you solve equations. Without that expression being equal to something, we can simplify, combine like terms, but we can't do much else with it.
"That dog don't hunt!" Is an example of a type of expression. Actually, it's a type that we're not really going to talk much about. In fact - I'm done.
In mathematics, there are other types of expressions. Algebraic, Analytic, Arithmetic, Closed-form, Mathematical, and Polynomial are all types of math expressions. Each of these types have their own elements and purposes. And since this section of this site is focused on Algebra 1, I am going to choose not to go into it.
In the very first section of this page I mentioned that expressions are made up of operators, constants, and variables, That's basically true, but they can also be made up of exponents, factorials, logarithms, different types of functions, integrals, and derivatives. Along with some things I have no doubt overlooked.
Let's take a look at this stuff. operators come in many flavors, the main ones are plus, minus, divide, and multiply.
Constants are symbols or numbers that represent a value that is not going to change. In the expression 3x + 16 the 3 is a constant as is the 16. Incidentally, in that expression we are multiplying 3 times x and adding 16 to it.
Variables are symbols that act as place holders for values that can change. In 3x + 16 the x is a variable. When x is 2 the expression becomes (3)(2) + 16 which is 6 + 16 or 22. When x is 3 the expression becomes (3)(3) + 16 or 25. Different values for the variable produce different results.
On the slightly more complex side. Exponents are covered in the section titled Exponents.. Logarithms are explained in Algebra II, and Derivatives and Integrals are used in Calculus. I do talk about Functions in the section on Functions.
Hopefully this made some kind of sense. If not, help me out and let me know. I am very open to any ideas that will make this site more functional.