Question 544617: how do you identify the terms, like terms, coefficients, and constants of this equation; 3+7x+3x+x
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  is an expression.
It is not an equation, because there is no equal sign equating one expression to another. Sometimes you need an expression as a recipe for calculating something, like the cost of doing business, that depends on changeable issues. That expression could mean the cost of a flower bunch with 7 red roses, 3 yellow ones and one white one, if x is the cost of one rose, no matter the color. The value of that expression may need to be recalculated if the price of a rose changes.
A part of an expression that's between + and/or - signs is called a term.
There are four terms in .
Like terms means similar terms. Since we do not know a value for x, we cannot calculate that expression, but we may be able to simplify it. There are three terms that have x in them. Those are like terms. We can add them together because it would be adding "apples to apples." You can pretend that instead of x it says "cereal bar" or "apple."
So, your expression simplifies like this:
Doing that is called "collecting like terms." It's like adding apples to apples and oranges to oranges. If you had  you could collect like terms like this:
It's as if x meant apple(s) and y meant orange(s).
Letters like x and y are called variables. Thay are usually used to represent something, like the price of a rose, that could vary.
The numbers multiplying those x and y symbols are called coefficients. If a coefficient is 1, we do not write it. The coefficient of one of your terms is 1. It is not written out, but we still say that the coefficient of that term is 1.
Numbers that are not multiplied times any letter variable, are called constants. Your expression has 3 as a constant. A constant is a term that has constant value. It does not change, like terms involving variables do.
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