Absolute values can be interpreted as the distance from a center point.
|t-750| < 250
Practice makes perfect
Absolute values can be interpreted as the distance away from a midpoint. For one-variable absolute value inequalities, this distance can be represented by two points on a number line. These are the endpoints of the given compound inequality.
Because our inequality needs a distance from a midpoint, we should find the halfway point between the endpoints. We can do this by calculating their mean.
Mean=500+ 1000/2= 750
Now we need to find the distance between this midpoint and each of the endpoints. To do this, we will find the difference between each of the endpoints and the midpoint.
distance= 750-500=1000- 750=250
We see that both 500 and 1000 are 250 units away from 750. Notice that the given inequality is an and inequality, and the symbols used can be read as less than.
500< t < 1000
500 is less than t
and
t is less than 1000
To write the given compound inequality as an absolute value inequality, we can show that the difference between a number t and the midpoint is less than the distance we found above.
|t- midpoint| < distance
|t- 750| < 250
