Evaluating expressions with one variable

Let's say we want to evaluate the expression $a + 4$a, plus, 4. Well, first we need to know the value of the variable $a$a. For example, to evaluate the expression when $\blueD {a = 1}$start color #11accd, a, equals, 1, end color #11accd, we just replace $\blueD a$start color #11accd, a, end color #11accd with $\blueD 1$start color #11accd, 1, end color #11accd:

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

We can just as easily evaluate $a + 4$a, plus, 4 when $\blueD {a = 5}$start color #11accd, a, equals, 5, end color #11accd:

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

You might be asked to "Evaluate $3x$3, x when $x = 5$x, equals, 5."

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

Okay, so now let's solve the problem:

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

Hold on a second! Did you notice that we wrote "$3$3 times $\blueD 5$start color #11accd, 5, end color #11accd" as $3 \cdot \blueD 5$3, dot, start color #11accd, 5, end color #11accd instead of as $3 \times \blueD 5$3, times, start color #11accd, 5, end color #11accd? Using a dot instead of the symbol $\times$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.

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:

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

Notice how we had to be careful to think about order of operations when evaluating. A common wrong answer is $\redD{32}$start color #e84d39, 32, end color #e84d39, which comes from first adding $5$5 and $3$3 to get $8$8 then multiplying $8$8 by $4$4 to get $\redD{32}$start color #e84d39, 32, end color #e84d39.