Algebraic expressions and equations:  this is where your work really begins to look and feel like algebra. You are about to begin working with letters of the alphabet as well as numbers and signs of operation. From now on, letters such as x, y, and z are just as common as numbers 1, 2, and 3.

So what do letters in algebra mean? Until now –- in basic arithmetic –- you worked with numbers, each number having a specific value or meaning. A "2" is a 2, for example. A "2" is always a 2 –- it is never a 6 and it is never a 10. It's like that for all numbers.  We still use regular arithmetic numbers in algebra,  but we also use terms expressed in letters. In algebra, the letter x, for example, can stand for a lot of different values. We can set x equal to 2 in one problem, but then set it equal to 6 in another. The letters in algebra can stand for an endless variety of values and combinations of values. Letters in algebra can even represent other letters.

Compare these two expressions:

• Arithmetic expression:  2 + 1
• Algebraic expression: x + 1

The arithmetic expression tells us to add 1 to the value of 2. The algebraic expression, however, covers a lot more territory by telling us to add a 1 to any value we choose. So if we let x = 2 in the algebraic expression, it becomes 2 + 1. If we let x = 5, it becomes the same as 5 + 1. You can see that the algebraic version is a lot more flexible than the arithmetic version.

The purpose of an equation is to express equality between the two expressions. And what is the real difference between an algebraic expression and an algebraic equations? Simple: An equation includes an equal sign (=) and an expression does not. An expression can include signs of operation, but not an equal sign.

Note: The main difference between an expression and an equation is that an equation includes an equal sign. An expression does not.