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:Part A) The number line in the attached figurePart B) The absolute value equation is  [tex]\left|x-7\right|=3[/tex]Step-by-step explanation:    Part A) Represent these two distances on a number linewe know thatThe minimum distance between two fence posts is 4 feet, and the maximum distance is 10 feetLetx ----> the distance between the two fence postso [tex]4\leq x \leq 10[/tex]The interval is -------> [4,10]using a graphing toolsee the attached figureIn 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 distancesFind the midpoint of the interval [4,10][tex]M=(\frac{x1+x2}{2})[/tex]substitute the values[tex]M=(\frac{4+10}{2})[/tex][tex]M=(7)[/tex]The distance from the midpoint to the endpoints of the interval is 3 feetsoThe absolute value equation is[tex]\left|x-7\right|=3[/tex]VerifySolve the absolute valuecase 1) positive value[tex]+(x-7)=3[/tex]Solve for x[tex]x=7+3=10\ ft[/tex] ----> maximum distance case 2) negative value[tex]-(x-7)=3[/tex]Solve for x[tex]-x+7=3[/tex][tex]x=7-3=4\ ft[/tex] ----> minimum distance