Absolute Value Equations
Absolute value is the distance of a number from 0 and is always positive. It’s denoted by a pair of vertical lines surrounding the value, such as the absolute value of 3. You can think of absolute value like you’re being asked a question and the question is: How far is 3 from 0? 3 is 1, 2, 3 places from 0.
The absolute value of 3 is 3. The absolute value of a negative number and its positive counterpart are the same. The absolute value of negative 3 is also 3, because negative 3 is also 3 places from 0. 1, 2, 3 places from 0. The absolute value of a difference, when you’re doing that, the order doesn’t matter.
Let’s look at the absolute value of a couple of differences. The absolute value of 8-3 and the absolute value of 3-8. When you’re doing the absolute value of a difference, again, the order doesn’t matter. The result will still be the same. Let’s see how that happens.
Start on the inside finding your difference. 8-3 is 5. We have the absolute value of 5. Again, absolute value is the distance from 0. 5 is 5 places from 0. Now, we’ll look at the difference switched around (3-8) 3-8, you could add the inverse of 3 plus negative 8. 3 plus a negative 8 is negative 5.
We have the absolute value of negative 5. Like we talked about over here, the absolute value of a number and it’s a negative counterpart are the same. The absolute value of 5 and negative 5 is the same, because, again, absolute value is the distance from 0 and distance can never be negative. The absolute value of negative 5 is also 5, since negative 5 is 5 places from 0.