Write an absolute value equation

Question

the Jesture accessory can recognize players when they are within a certain range. The player's distance from the Jesture can vary up to 1.2 meters from the target distance of 2.4 meters.

Write an absolute value equation that can be used to find the extreme distances that a player can stand from the Jesture and still be recognized.

Solve your equation, and interpret the solutions.

Answer 1

Let x = player distance from Jesture.  Jesture can recognize players in the range of 2.4 meters ± 1.2 meters.

 

(2.4 m - 1.2 m) ≤ |x| ≤ (2.4 m + 1.2 m)

 

1.2 ≤ |x| ≤ 3.6

 

Solution is:

 

1.2 ≤ x ≤ 3.6

and

-3.6 ≤ x ≤ -1.2

 

In interval notation: [-3.2,-1.2]U[1.2,3.6]

 

   -4       -3     -2     -1     0     1      2      3        4    5

<--|--[---|----|---]-|----|----|-[---|----|---]--|----|-->

 

Where x=0 is the position of Jesture.