Solving one step equations can be a very simple process! This is the
beginning to solving much more complex mathematical problems. Before we can
go into solving these equations there are a few terms you need to know.
 VARIABLE- a “mystery” number that is represented by a letter from the
alphabet. This letter in Algebra is usually an x. Do not confuse the variable x
with the multiplication symbol. Multiplication in Algebra is usually
represented with a •. For example 2•2=4. A number standing next to a
variable represents multiplication in Algebra. For example 2x means 2 times
x.
 COEFFICENT- The number standing next to the variable. For example the
coefficient of 2x is 2 because the 2 is standing right next to the variable.
 EQUATION- Any mathematical statement that contains an equal sign. For
example 2x = 2 is an equation because there is an equal sign, but 4x is not
because there is no equal sign.
 INVERSE- literally means the opposite. The inverse of addition is subtraction
and the inverse of subtraction is addition. Furthermore the inverse of
multiplication is division and the inverse of division is multiplication.
There are two things that you must be able to do when simplifying algebraic expressions. The
first is to be able to use the distributive property.
The second math concept that you must understand is how to combine like
terms.
So, what are like terms? Let's start first with just the word, term and a few other
vocabulary words!
2x, 5y, 7, 3xy, 4, 8x, 6y, 4x2
Take a look at the 8 terms above. (2x is a term, 5y is a term, 7 is a term...)
The 4 and the 7 do not have a variable. They are called constants. Since they don't
have a variable, their values will always remain the same, 4 and 7. That's why they
are called constants.
The 2 in the term 2x is called a coefficient. A coefficient is a number by which a
variable is multiplied. The 5 in the term 5y is a coefficient; The 3 in the term 3xy is
a coefficient.
Can you guess which other terms have coefficients?
Yes, you are right, the 8 in 8x, 6 in 6y, and the 4 in 4x2.
Ok.. now moving onto like terms. Like terms are two or more terms that have
EXACTLY the same variables. (The coefficients do not have to be the same, just
the variables!)
For example, for the 8 terms above, 2x and 8x are like terms because they both
just contain an x.
Can you find the other two sets of like terms?
Yes, 5y and 6y are like terms. 7 and 4 are like terms because they are both
constants.
3xy does not have a like term because no other term has the variable x and y. 4x2
does not have a like term because no other term has x2.
TIP: When you combine like terms, you MUST take the sign in front of the term
with it or your answer may be incorrect!
Ok, are you confident enough to use the distributive property when simplifying
algebraic expressions? Sure you are, let's go!
If you see an addition or subtraction problem inside a set of parenthesis, you
must use the distributive property BEFORE simplifying the expression.
As you review the next 2 examples, notice how the distributive property was used
first, then the algebraic expression was simplified.
Ok... with four great examples, you should be ready to try some on your own!