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 (THERES ALOT OF ANSWERS BE PREPARED) SELECT ALL THE ANSWER CHOICES.

4pm,

8pm,

9am,

3pm,

noon,

11am,

6pm,

9pm,

7am,

1pm,

2pm,

5pm,

10pm,

10am,

8am,

7pm,

6am,

Answer 1

8 pm and 8 am

Explanation:

Let us solve the equation

`2|(x-2)|-12=0`

There is a modulus in the equation this means that one value of the modulus will be positive and the other will be negative

Let us solve for the positive first

`2(x-2)-12=0\\\Rightarrow 2x-4-12=0\\\Rightarrow x=(16)/(2)\\\Rightarrow x=8`

Now we add this value with 12 noon

So

`12+8=8\ \text{pm}`

Let us solve for the negative

`2(-(x-2))-12=0\\\Rightarrow 2(2-x)-12=0\\\Rightarrow 4-2x-12=0\\\Rightarrow x=-(8)/(2)\\\Rightarrow x=-4`

So

`12-4=8\ \text{am}`

The times when the serving time is as advertised is 8 pm and 8 am.