Answer:
Part A) The number line in the attached figure
Part B) The absolute value equation is
Step-by-step explanation:
Part A) Represent these two distances on a number line
we know that
The minimum distance between two fence posts is 4 feet, and the maximum distance is 10 feet
Let
x ----> the distance between the two fence post
so
The interval is -------> [4,10]
using a graphing tool
see the attached figure
In a number line the solution is the shaded area at right of x=4 (close circle) and at the left of x=10 (close circle)
Part B) Write an absolute value equation that represents the minimum and maximum distances
Find the midpoint of the interval [4,10]
substitute the values
The distance from the midpoint to the endpoints of the interval is 3 feet
so
The absolute value equation is
<em>Verify</em>
<u>Solve the absolute value</u>
case 1) positive value
Solve for x
----> maximum distance
case 2) negative value
Solve for x
----> minimum distance
