# Evaluating Variable Expressions

- -

A variable is a letter which is used to represent a number or a set of numbers. It is usually denoted by a letter of the English alphabet. Greek letters too can denote a variable. Examples of variables are x, y, r, s, t, and n.

Greek letters such as $\alpha$, and $\beta$ can be used also to denote a variable.

An algebraic expression is a combination of arithmetic operations, numbers, and variables. An algebraic expression may include grouping symbols. The following are examples:

$-2x$, $4x+7y$, and $\frac{3x+y}{4y+3-2}$.

The parts separated by + or - signs are terms. In our examples mentioned above, $-2x$ and $\frac{3x+y}{4y+3-2}$ have one term while $4x+7y$ has two terms.

To evaluate an algebraic expression substitute the given value(s) of the variable(s) then use the order of operations (PEMDAS) to find the value of the resulting numerical expression.

Examples:

Evaluate the following variable expressions.

1. $3y+4$, for $y=2$
2. $4x-4y+3z$, for $x=0$, $y=2$, $z=3$

Solutions:

1. $3y+4=3(2)+4=6+4=10$
2. $4x-4y+3z=4(0)-4(2)+3(3)=0-8+9=1$