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### Course: Algebra (all content) > Unit 1

Lesson 2: Introduction to variables# 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 $a+4$ . Well, first we need to know the value of the variable $a$ . For example, to evaluate the expression when ${a=1}$ , we just replace ${a}$ with ${1}$ :

So, the expression $a+4$ equals $5$ when $a=1$ .

We can just as easily evaluate $a+4$ when ${a=5}$ :

So, the expression $a+4$ equals $9$ when $a=5$ .

## Evaluating an expression with multiplication

You might be asked to "

**Evaluate**$3x$ when $x=5$ ."Notice how the number $3$ is right next to the variable $x$ in the expression $3x$ . This means "$3$ times $x$ ". The reason we do this is because the old way of showing multiplication with the symbol $\times $ looks confusingly similar to the variable $x$ .

Okay, so now let's solve the problem:

So, the expression $3x$ equals $15$ when $x=5$ .

### New ways to show multiplication

Hold on a second! Did you notice that we wrote "$3$ times ${5}$ " as $3\cdot {5}$ instead of as $3\times {5}$ ? Using a dot instead of the symbol $\times $ 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 |

## 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**$5+3e$ when ${e=4}$ .

So, the expression $5+3e$ equals $17$ when $e=4$ .

Notice how we had to be careful to think about order of operations when evaluating. A common wrong answer is ${32}$ , which comes from first adding $5$ and $3$ to get $8$ then multiplying $8$ by $4$ to get ${32}$ .

## Let's practice!

## Challenge problems

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