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

we can think of the variable b as books.  So, we can write the problem as

So, we can read the problem like this:  We have borrowed 2 books from the library.  We go back to the library and borrow 5 more books.  How many total books have we borrowed from the library?  We have borrowed 7 books.  So,

We add variables the same way.

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

So, in the problem

we can think of the variable p as potatoes.  So, we can write it like

We can read the problem like this:  We go to the store to buy 5 potatoes.  We realize we need more, so we buy 5 more potatoes.  How many potatoes did we buy in total?  We bought 10 potatoes.  So,

We can add variables the same way.

When adding variables, we will look at the variables like objects.  So, in the problem

we can think of the variable p as pictures.  So, we can write it like this:

We can read it like this:  We have taken 9 pictures with our new camera.  We walk around for a while, and we take 6 more pictures.  How many pictures have we taken in total?  We have taken 15 pictures.  So,

We add variables the same way.  So,

When adding variables, we will look at the variables like objects.  So, in the problem

we can think of p as pancakes.  So, we can write it like

We can read the problem like this:  We are eating breakfast.  We are very hungry, and we decided to eat 2 pancakes.  We are still hungry, so we eat 3 more pancakes.  How many pancakes have we eaten for breakfast? We have eaten 5 pancakes.

We can add variables the same way.

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

we can think of the variable p as pretzels.  So, we can write it like

We can read the problem like this:  We eat 2 pretzels.  They are really good, so we eat 5 more pretzels.  How many pretzels have we eaten in total?  We have eaten 7 pretzels.

We can add variables the same way.  So,

When adding terms with variables, we can only combine the terms with like variables.  So, we get

To add variables, we will combine like variables together.  We can also think of the variables as objects.  

For example, a could be apples, and b could be balloons.  So, we could write

To solve this problem you must combine all of the like terms.

So we add 

.

Then we add those together to simplify the expression to 

.

First, combine all like terms, so we are left with 

.

Then to isolate the variable (get it alone), we divide each side by 10 and are left with 

.

Simplify by combining like terms.

We can begin by reordering our variables to have ones with the same exponent next to eachother.

Then, simply add the cofficients (numbers in front of the variables) of any variable with the same exponent

So our answer is: