write the compound inequality 3.1 less then or equal to m less than or equal 4.7 as an absolute value inequality.
To write the compound inequality "3.1 less than or equal to m less than or equal to 4.7" as an absolute value inequality, you need to find the midpoint between the endpoints and the distance between the midpoint and either endpoint.
First, find the midpoint between 3.1 and 4.7:
Midpoint = (3.1 + 4.7) / 2
Midpoint = 7.8 / 2
Midpoint = 3.9
Next, find the distance between the midpoint and either endpoint:
Distance = (4.7 - 3.9) / 2
Distance = 0.8 / 2
Distance = 0.4
Finally, write the absolute value inequality using the midpoint and distance:
|m - 3.9| ≤ 0.4
This absolute value inequality is equivalent to the given compound inequality "3.1 ≤ m ≤ 4.7".