# Evaluating expressions with one variable

A mixture of explanations, examples, and practice problems to have you evaluating expressions with one variable in no time!

# How to evaluate an expression with one variable

Let's say we want to evaluate the expression . Well, first we need to know the value of the variable . For example, to evaluate the expression when , we just replace with :

So, the expression equals when .

We can just as easily evaluate when :

So, the expression equals when .

# Evaluating an expression with multiplication

Here's a problem you might see:

Evaluate when .

Notice how the number is right next to the variable in the expression . This means " times ". The reason we do this is because the old way of showing multiplication with the symbol looks confusingly similar to the variable .

Okay, so now let's solve the problem:

So, the expression equals when .

### New ways to show multiplication

Hold on a second! Did you notice that we wrote " times " as instead of as ? Using a dot instead of the symbol is another new way of showing multiplication:

Parentheses can also be used to show multiplication:

Let's summarize the new ways of showing multiplication that we learned.

Old way | New way | |
---|---|---|

With a variable | ||

Without variable | or |

# Evaluating expressions where order of operations matter

For more complex expressions, we'll have to be sure to pay close attention to order of operations. Let's take a look at an example:

**Evaluate when .**

.

So, the expression equals when .

Notice how we had to be careful to think about order of operations when evaluating. A common wrong answer is , which comes from first adding and to get then multiplying by to get .