The most important thing I want you to remember after reading this is that absolute value is a measurable distance.
The second most important thing I want you to remember is that absolute value is positive most of the time. (This is because distance is generally a positive measurement.
Absolute value is indicated by two long straight lines | |. This means you’re trying to find how far you are from 0. For example, |4| is four units from 0, and it therefore it equals 4. If you’re dealing with |-4|, that’s also 4 units away from 0, so it also equals 4.
That’s it…that’s all there is to absolute value. Of course, then you have to learn how to apply it.
Let’s say you’re given the problem -| -6|. You know the absolute value of -6 is 6, but because there’s a negative sign outside the absolute value signs, it stays with the 6 for an answer of -6.
Equations sometimes have absolute value in them. Look at the following: |2x – 4| = 8 Because the equation inside the absolute value signs can be positive or negative, we have to solve for both answers.
2x – 4 = 8 2x – 4 = -8
2x = 12 2x = -4
x = 6 x = -2
The solution to |2x – 4| = 8 is both 6 and -2.
Absolute value can also show up in inequalities. Let’s look at |3x + 9| > 6 Again, we have to solve two equations, and we have to pay very close attention to the set-up.
3x + 9 > 6 3x +9 < -6
3x > -3 3x < -15
x > -1 x < -5
Note that when we set the second equation to the negative answer, we also flipped the inequality sign. Our solution is x > -1 or x < -5. If we were to graph this out, we would have a broken line with a gap between -1 and -5.
If you’re not sure you did the inequality correctly, you can always pick a number that would make the sentence true and check your work. If it doesn’t make a true statement once you simplify the problem, you probably have the inequality sign going the wrong way.
That’s it for this week. If you have any suggestions for next week, or questions about work you’re doing in school, feel free to drop us a line at deadbunnyed@gmail.com.
