An algebraic expression represents a quantity using numbers, variables and operations. A variable is a symbol whose value may change or may not yet be known. For example,

$$3x+2$$

is an expression whose value depends on $x$.

Terms and coefficients

Expressions are built from terms, which are separated by addition or subtraction. In

$$5x-3y+7,$$

$5x$, $-3y$ and $7$ are the terms. The numbers multiplying variables are their coefficients, so the coefficients of $x$ and $y$ are $5$ and $-3$.

Evaluating expressions

To evaluate an expression, replace each variable by a value and carry out the operations. If $x=4$, then

$$3x+2=3(4)+2=14.$$

The usual order of operations determines which operations are performed first.

Equivalent expressions

Different expressions can represent the same quantity. The distributive property gives

$$2(x+3)=2x+6,$$

and like terms can be combined:

$$3x+2x=5x.$$

Rewriting an expression in an equivalent form changes its appearance without changing its value. An equation, by contrast, states that two expressions are equal; for example, $3x+2=14$.