Evaluating an Expression

Date: 03/28/2001 at 18:50:05
From: Bob
Subject: Hands-on Equations

How do you solve an equation like: if x = 6, evaluate 2x+3*+4 = ? 

That may not be possible because it isn't the problem I am looking at. 
I just don't know how to do this kind of problem. I can figure out 
what x or star is, but I don't know how to "evaluate."

Date: 03/29/2001 at 12:50:21
From: Doctor Peterson
Subject: Re: Hands-on Equations

Hi, Bob.

The key is to know what "evaluate" means: it means to find the value 
of an expression. In other words, you simply replace the variable with 
its value, and then do what the expression says to do. (Incidentally, 
what you're doing here is NOT "solving an equation"; that's what 
you do when you are given an equation, such as 2x + 4 = 3, and asked 
to find what x is. Here you are "evaluating an expression," which is 
almost the opposite.)

In your example, I'm going to suppose that the asterisk should have 
been an x, since you seem to be thinking of it as a variable, but you 
haven't given it a value. We can only evaluate an expression when we 
know the values of all the variables.

Let's evaluate:

     2x + 3x + 4

To do this, with x = 6, you just replace x with 6. You can actually 
write this out, if you want; I recommend using parentheses around the 
value, because in some problems you'll see later that can save a lot 
of confusion:

     2(6) + 3(6) + 4

Now do what it says. First multiply 2 by 6 and 3 by 6:

     12 + 18 + 4

Now add:

     34

That's the value of your expression when x is 6. If you're not 
familiar with the order in which you should add and multiply here, see 
our FAQ on Order of Operations at:

   http://mathforum.org/dr.math/faq/faq.order.operations.html   

There's one other important thing you can do with an expression: 
simplify it. That means that you don't know the values of the 
variables, but you want to make it easier to evaluate when you do - 
sort of predigesting the expression. In this example, you have two 
multiples of x (I deliberately made it that way), so we can combine 
them using the "distributive property," which just says that 2 of 
something and 3 of the same thing is the same as 5 of them:

       2x + 3x + 4
     = (2 + 3)x + 4
     = 5x + 4

Now when we evaluate it, we have less work to do; 5 times 6 is 30, 
plus 4 is 34. That's why we call this simplifying.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/