Exercise 16 Page 32

An absolute value measures an expression's distance from a midpoint on a number line. |q-8|= 14 This equation means that the distance is 14, either in the positive direction or the negative direction. |q-8|= 14 ⇒ lq-8= 14 q-8= - 14 To find the solutions to the absolute value equation, we need to solve both of these cases for q.

|q-8|=14

lc q-8 ≥ 0:q-8 = 14 & (I) q-8 < 0:q-8 = - 14 & (II)

lcq-8=14 & (I) q-8=- 14 & (II)

(I), (II): LHS+8=RHS+8

lq_1=22 q_2=- 6

Both 22 and - 6 are solutions to the absolute value equation. Let's graph these solutions on a number line.