The minimum distance between two fence posts is 4 feet. the maximum distance is 10 feet. a. represent these two distances on a number line. b. write an absolute value equation that represents the minimum and maximum distances

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

Verify

Solve the absolute value

case 1) positive value

Solve for x

----> maximum distance

case 2) negative value

Solve for x

----> minimum distance

entering that problem on the tube might get you an answer