Exercise 58 Page 34

We are asked to come up with a situation that can be modeled by an absolute value equation. Let's pretend that average number of hours you need to work each month to get school credit for your internship is 67. Your boss tells you that he will sign your paperwork as long as you fall within 5 hours of the required 67 hours. Let's picture the number of hours we need to work in order to get credit on a number line.

If we want to find the minimum and maximum number of hours worked, we can model this situation with an absolute value equation, where the minimum and maximum number of hours are the solutions. |x-Midpoint|&=Distance In the equation the midpoint is a point at an equal distance from both solutions, and the distance is the distance between the midpoint and either one of the solutions. We can substitute those values into the equation. |x-Midpoint|&=Distance |x- 67|&= 5 Let's solve for the minimum and maximum number of hours by splitting the absolute value into two cases.

| x-67|=5

lc x-67 ≥ 0:x-67 = 5 & (I) x-67 < 0:x-67 = - 5 & (II)

lcx-67=5 & (I) x-67=- 5 & (II)

(I), (II): LHS+67=RHS+67

lx=72 x=62

We then know that we need to work a minimum of 62 hours and a maximum of 72 hours each month. Keep in mind that this is just one possible solution and your answer may be different.