Question

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

Answer 1

Answer:

Part A) The number line in the attached figure

Part B) The absolute value equation is  $\left|x-7\right|=3$

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

$4\leq x \leq 10$

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]

$M=(\frac{x1+x2}{2})$

substitute the values

$M=(\frac{4+10}{2})$

$M=(7)$

The distance from the midpoint to the endpoints of the interval is 3 feet

so

The absolute value equation is

$\left|x-7\right|=3$

Verify

Solve the absolute value

case 1) positive value

$+(x-7)=3$

Solve for x

$x=7+3=10\ ft$ ----> maximum distance

case 2) negative value

$-(x-7)=3$

Solve for x

$-x+7=3$

$x=7-3=4\ ft$ ----> minimum distance