CCSS Math: 6.EE.A.2, 6.EE.A.2c
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+4a + 4. Well, first we need to know the value of the variable aa. For example, to evaluate the expression when a=1\blueD {a = 1}, we just replace a\blueD a with 1\blueD 1:
a+4=1+4        Replace a with 1.=5\begin{aligned} &\blueD a + 4 \\\\ =&\blueD1 + 4~~~~~~~~\gray{\text{Replace }\blueD{a} \text{ with } \blueD{1}\text{.}} \\\\ =&5 \end{aligned}
So, the expression a+4a + 4 equals 55 when a=1a = 1.
We can just as easily evaluate a+4a + 4 when a=5\blueD {a = 5}:
a+4=5+4        Replace a with 5.=9\begin{aligned} &\blueD a + 4 \\\\ =&\blueD5 + 4~~~~~~~~\gray{\text{Replace }\blueD{a} \text{ with } \blueD{5}\text{.}} \\\\ =&9 \end{aligned}
So, the expression a+4a + 4 equals 99 when a=5a = 5.

Evaluating an expression with multiplication

You might be asked to "Evaluate 3x3x when x=5x = 5."
Notice how the number 33 is right next to the variable xx in the expression 3x3x. This means "33 times xx". The reason we do this is because the old way of showing multiplication with the symbol ×\times looks confusingly similar to the variable xx.
Okay, so now let's solve the problem:
3x=35        Replace x with 5.=15\begin{aligned} &3\blueD x \\\\ =& 3 \cdot \blueD5~~~~~~~~\text{Replace }\blueD{x} \text{ with } \blueD{5}\text{.} \\\\ =&15 \end{aligned}
So, the expression 3x3x equals 1515 when x=5x = 5.

New ways to show multiplication

Hold on a second! Did you notice that we wrote "33 times 5\blueD 5" as 353 \cdot \blueD 5 instead of as 3×53 \times \blueD 5? Using a dot instead of the symbol ×\times is another new way of showing multiplication:
35=153 \cdot \blueD 5 = 15
Parentheses can also be used to show multiplication:
3(5)=153(\blueD 5) = 15
Let's summarize the new ways of showing multiplication that we learned.
Old wayNew way
With a variable3×x3 \times x3x3x
Without variable3×53 \times 5353\cdot 5 or 3(5)3(5)

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+3e5 + 3e when e=4\blueD{e=4}.
5+3e=5+34        Replace e with 4.=5+12        Multiply first (order of operations)=17\begin{aligned} &5+3\blueD e \\\\ =&5 + 3 \cdot \blueD 4~~~~~~~~\gray{\text{Replace }\blueD{e} \text{ with } \blueD{4}\text{.}} \\\\ =&5 + 12 ~~~~~~~~\text{\gray{Multiply first (order of operations)}} \\\\ =&17 \end{aligned}
So, the expression 5+3e5 + 3e equals 1717 when e=4e = 4.
Notice how we had to be careful to think about order of operations when evaluating. A common wrong answer is 32\redD{32}, which comes from first adding 55 and 33 to get 88 then multiplying 88 by 44 to get 32\redD{32}.

Let's practice!

Problem 1
Evaluate the expression 9z9 - z when z=4z = 4.

Challenge problems

Challenge problem 1
Evaluate ee5ee \cdot e - 5e when e=5e=5.