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/
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