[Music] today we'll be talking about the addition property of equality now when we are solving one-step equations we need to remember that what we do on one side of the equation we need to do on the other side of the equation this allows us to make sure that we maintain the integrity of the equal sign so when i look at my first problem here i ask myself what number is attached to the variable the variable is the letter and so we could say it is attached by a five now what is holding that five together and it is a negative so an opposite of a negative 5 is a positive 5. so we're going to go ahead and not multiply but we're going to add 5 to both sides of the equation now once we have done that we go ahead and bring the variable down and this is the letter m now we know that negative five and positive five are inverses of each other and so that is going to equal zero and so it would be m plus 0 but we could go ahead and drop that 0 off and then 9 plus 5 is 14. that is just a simple one step property addition property of equality this is also known as a one-step equation so let's go ahead into the second problem the second problem we notice that the variable and the constant are in reverse order that's not going to be a problem if we will treat it just exactly the same and so we ask ourselves what is attached to the negative 12 or attached to b and that is the negative 12. so what is the opposite or the inverse of negative 12. it's a positive 12. so in this addition property of equality what i do on one side of the equation i will do on the second side of the equation so i'm going to add 12 to the second side as well now we go ahead and we realize that a negative 12 and a positive 12 are inverses of each other and so a negative 12 plus 12 is going to be zero which brings our variable down we are going to keep our equal signs in line with each other and now we have 17 plus 12. 7 plus 2 is 9 1 plus 1 is 2. so in this answer is b equals 29 now i'm going to take another step and let's go back and check our work so we want to double check our work to make sure it is correct so wherever i see my variable i'm going to go ahead and put the number 14. 14 minus 5 equals 9 and 14 minus 5 is 9 and since 9 equals 9 we know that that is going to check out now let's go ahead and see our second problem and see if that checks out so wherever i see i see my negative 12. plus i'm going to add 29 and then that is going to equal 17. so i look at when i combine these integers together i have 29 positives and 12 negatives which allows me which i have 17 positives is equal to a positive 17 on this side so both of these equations check out i checked my work when you are doing the addition property of equality make sure what you do on one side of the equation you do on the same side of the opposite side of the equation and these are easy one step problems for [Music] you [Music] you