Step-by-step explanation:
Given Ben's observations when the wait time is as advertised represented by the equation 2|x − 2| − 12 = 0, to get the times when the serving time is as advertised, relative to noon, we will calculate for the value of x in the equation;
Note that the modulus of the function |x-2| will return both positive and negative value.
For the positive value of |x-2|;
2|x − 2| − 12 = 0
2(x − 2) − 12 = 0
open the parenthesis
2x-4 - 12 = 0
2x - 16 = 0
add 16 to both sides
2x-16+16 = 0+16
2x = 16
x = 16/2
x = 8
For the negative value of |x-2|;
2|x − 2| − 12 = 0
-2(x − 2) − 12 = 0
open the parenthesis
-2x+4 - 12 = 0
-2x - 8 = 0
add 8 to both sides
-2x-8+8 = 0+8
-2x = 8
x = -8/2
x = -4
Hence the times when the serving time is as advertised, relative to noon are 8minutes and 4minutes
