The ability to work comfortably with negative numbers is essential to success in algebra. For this reason, we will do a quick review of adding and subtracting positive and negative integers. Integers are all the positive whole numbers, zero, and their opposites (negative numbers).
When adding integers, we have two cases to consider. The first case demonstrates a situation with matching signs: both integers are either positive, or both integers are negative. If the signs match, we will add the numbers together, and keep the sign. This is illustrated in the following examples:

Same sign, add , keep the negative  

Our Solution  
 

Same sign, add , keep the negative  

Our Solution 
The second case demonstrates a situation with signs that don't match (one integers is positive and one integer is negative). We will subtract the numbers (as if they were all positive), and then use the sign from the larger number. This means if the larger number is positive, the answer is positive; and if the larger numbers is negative, the answer is negative. This is shown in the following examples:

Different signs, subtract , use sign from bigger number, negative  

Our Solution  
 

Different signs, subtract , use sign from bigger number, positive  

Our Solution  
 

Different signs, subtract , use sign from bigger number, positive  

Our Solution  
 

Different signs, subtract , use sign from bigger number, negative  

Our Solution 
For subtraction of negative numbers, we will change the problem to an addition problem, which can then be solved using the above methods. The way we change subtraction to addition is to add the opposite of the number after the subtraction sign. Often this method is referred to "adding the opposite." This is illustrated in the following examples:

Add the opposite of  

Different signs, subtract , use sign from bigger number, positive  

Our Solution  
 

Add the opposite of  

Same sign, add , keep the negative  

Our Solution  
 

Add the opposite of  

Same sign, add , keep the positive  

Our Solution  
 

Add the opposite of  

Different sign, subtract , use sign from bigger number, negative  

Our Solution 
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT: HTTP://WALLACE.CCFACULTY.ORG/BOOK/BOOK.HTML