Objectives:
- Define absolute value.
- Determine the absolute value of a number.
- Simplify expressions containing absolute value.
What is absolute value?
Absolute value is the distance from zero on the number line.
Absolute value is the distance from zero on the number line.
For example, the following image shows that the absolute value of -6 is the distance from 0 and -6 on the number line. This distance is 6.
Distance is always POSITIVE!
Example #1
We can determine the absolute value of -10 by looking at the number line.
From the image above, we can see that the distance from 0 and -10 on the number line is 10.
Example #2
Notice the negative outside of the absolute value bars. This tells me that my answer will be negative. Please note that this does not mean distance is negative. Again, distance is always positive. The negative is outside of the absolute value bars so it does associate with distance. The value inside of the absolute value bars will always be positive.
The distance from 0 to -5 on the number line is 5. Since there is a negative outside of the absolute value bars, the outcome will be negative.
Example #3
The 2 in front of the absolute value is being multiplied by the absolute value of -8. Since the absolute value of -8 is 8, we can rewrite the problem:
Example #4
For this last example we will look at how to simplify absolute value expressions.
Your Turn
Simplify the following:
