When adding variables together, you must first make sure you are combining the same variable.  So, in this case

we can see that both terms contain the variable a.  Therefore, we can combine them. 

Now, when we combine them, we can think of the variables as objects.  So, we can say were are combining an apple and 4 apples together.  So,

We can simplify our problem the same way.

Combine the following variables:

First, group the like terms. This means we will put terms with the same exponent next to each other. This will make it easier to be sure we are adding correctly.

Next, add the coefficients, but keep the exponents the same. Only combine terms with the same exponents. Notice that we have three different exponents (6,5 and 2) This means we will have three terms in our final answer.

So we get the following:

To add variables, we will think of the variables as objects.  So, in the problem

let's think of the variable x as books.  So, we can look at the problem as we currently have 3 books.  We go to the library and borrow 7 more books.  How many books do we have now?  The answer is 10.  We now have 10 books.  

We can add the variables in the same way.  So,

To add variables, we will look at the variables as objects.  So, 

we can look at it as the following.  We have 6 dollars.  We do all of our chores, and we get 4 more dollars.  How many dollars do we have now?  We now have 10 dollars.  We add variables in the same way. So

When we add variables, we can think of the variables as objects.  So in the problem,

we can think of the variable a as apples.  We can say that we currently have 5 apples.  We go to the store and buy 6 more apples.  How many apples do we have now?  We have 11 apples.  

We can add variables the same way.  So,

Combine the following terms.

We need to realize that we can only add variables together if they have the same exponent. Then, all we need to do is add the coefficients (numbers in front)

So, let's reorganize our statement to have variables of the same power together

Now, we can add the first two and last two to get our answer

To add variables, we will look at the variables like objects.  So in the problem

we will think of a as being apples.  So we can read this problem as

So, if we have 3 apples, and we go to the market and we buy 6 more apples, how many apples do we now have?

We add variables the same way.  So,

We can look at this as we have 3 of something, we want to add 6 more somethings, so how many do we have now?

In the problem

we will first insert a coefficient on the second term.  When a variable stands alone, it has a coefficient of 1.  So,

When adding variables, we can look at the variables as objects, then combine those objects.

Now, we can think of the variable a as cars. So, we can look at it as

We can think of it like this:  If we see 5 cars pass by us on the road, and we see 1 more car pass us, how many cars have passed us?  The answer is 6.  There were 6 cars that passed us.  So,

We add variables the same way.

When adding variables, we can look at the variables as objects.  So, in the problem

we can think of x as books.  So, we can write it like this

We can think of it like this.  We have 4 books and we borrow 2 more books.  How many books have we borrowed?  

We have borrowed 6 books.  

We can add variables the same way.

When adding variables, we can look at the variables as objects.

So, in the problem

we can think of the variable a as apples.  So, we can write it like

We can think of the problem like this:  We have 2 apples, and we go to the store and buy 3 more apples.  How many apples do we have now?  We have 5 apples.  So, we can solve it like

We add variables the same way.  So,