Question

Ben’s favorite deli says the average serving time is 12 minutes. Ben notices that the wait time at the deli varies at different times of day, before and after noon. His observations when the wait time is as advertised can be represented by the equation 2|x − 2| − 12 = 0. Solve for the times when the serving time is as advertised, relative to noon. Group of answer choices 7 AM 6 PM 4 PM 1 PM 10 PM 3 PM 7 PM 9 PM 10 AM 6 AM Noon 5 PM 2 PM 8 AM 11 AM 8 PM 9 AM

Answer 1

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