Study Guide

Evaluating Algebraic Expressions

Evaluating Algebraic Expressions

Expressions are made of variables, or letters that take the place of unknown numbers. But what if we know the numbers? We can take out the variable, replace it with the number, and do the math. This is called evaluating an algebraic expression.

If we have the expression 3x + 1 and we find out that x = 10, we can evaluate it. The expression means "three times whatever x is, plus one."

We rewrite the expression, replacing the x with 10 in parentheses, and do the math.

3x + 1 =
3(10) + 1 =
30 + 1 =
31

Sample Problem

Evaluate 4xy + 3x if x = 8 and y = 5.

We take out all the variables and put in the numbers in parentheses. Replace x with 8 and swap out y with 5.

4xy + 3x =
4(8)(5) + 3(8) =
160 + 24 = 184

Don't Forget: we'll need our faithful friend PEMDAS (a.k.a. the Order of Operations) to make sure we do the math in the right order.