Absolute Value

It is impossible for all of us not to have heard about the Absolute Value at least once in our lives. Some of us may have found it an easy-to-understand topic, while some of us may have found it a difficult topic. Nonetheless, just like every other topic in Mathematics, Absolute Value is a very important topic which we should pay meticulous attention to. In this article, our goal is to explain what Absolute Value is.

One important note before we move on to the topic: when we deal with numbers, it is very important to try to always refer to the number line since it will make our life tremendously easy in understanding every topic related to numbers. Now, let’s move on…

When we take the absolute value of a certain number, let it be either positive or negative, what we really do is see how far is that number from zero. For example, the absolute value of 5 is equal to 5, as the absolute value of -5 is equal to 5. As already said, in order to better understand the absolute value, think of the number line and the distance that both 5 and -5 have from zero. Both 5 and -5 have the same distance (if we may call it distance) from 0. With this being said, we understand that the absolute value of a number is the positive version of that number.

Under the same logic we can solve absolute value equations. For example, let’s take the absolute value of x-15 which equals to 10. How do we solve it? When solving absolute value equations, we should always take both the positive value and the negative value of the expression within the absolute value. So, we take x-15 = 10 (let’s name it equation 1) or –(x-15) = 10 (let’s name it equation 2). Now, let’s solve both equations. For equation 1, x=25, while for equation 2, x=5. The next step is to plug the values of x. Equation 1: the absolute value of 25-15 = 10, which is correct. Equation 2: the absolute value of 5-15=10, which is also correct.

Now that we know what the Absolute Value stands for and the process of how to solve absolute value equations, we are ready to move to linear equations. Good luck.