How to solve basic algebraic equations with the properties of equality: Addition and Subtraction

When you first see x-4=8, you might instantly know the answer. But do you know how to show how you got your answer?

Let’s look at the equation. We want to have x on one side and all the other numbers and operations on the other side. Now, this may sound a little confusing, so I’ll explain further.

We want to get rid of the -4 in x-4=8 so that we can immediately have our answer, x= something. We can’t have -4 in the way because x-4=8 is not giving us the answer. So in order to get rid of the -4, we have to use the inverse operation, addition.

x-4=8

+4

Now, if we add +4 to the equation, we have x=8. This answer is obviously not correct, for 8-4 does not equal 8. The reason the answer is not correct is because we have not added +4 to 8.

Why do we have to add +4 to 8? There is a rule when dealing with equation. Whatever you do on one side, you also have to do on the opposite side. So in this case, we have to add 4 to 8 because we have added 4 to -4.

x-4=8

+4 +4

Since we have finished adding 4 to both -4 and 8, we now have our answer. X is now on one side, -4 is gone because we have added 4 to it, and our value of x, 12, thanks to the equality rule. So in summary, x-4=8 has changed into x=12-4=8. Let’s see if we are correct.

12-4=8.

Yup, it’s correct! Make sure to check each answer you get by plugging it back in your equation afterward. Think of plugging in a charger. When you charge your phone or device, you connect them together to solve the problem, low battery. Pretend the charger is the answer or value of a variable like y. Plugin the charger and when you get the right value, think of the pop-up, “Charging.”

Here is a short quiz: https://www.cliffsnotes.com/study-guides/basic-math/basic-math-and-pre-algebra/variables-algebraic-expressions-and-simple-equations/quiz-solving-simple-equations

Some questions are laid out in a different way, so it’s okay if you make a mistake. Email me questions at shannonkaho@gmail.com and if you know me, you can simply just message me and we can schedule a zoom time. 🙂

When you have a different operation like addition, subtract. But when you have multiplication and division, it’s a bit different but has the same concept. I’ll explain in my next post, which will hopefully be posted soon! Bye and have a great day!