Exercise 35 Page 86

An absolute value measures an expression's distance from a midpoint on a number line. |d/9|= 6 This equation means that the distance is 6, either in the positive direction or the negative direction. |d/9|= 6 ⇒ ld/9= 6 d/9= - 6 To find the solutions to the absolute value equation, we need to solve both of these cases for d.

|d/9|=6

lc d/9 ≥ 0: d/9 = 6 & (I) d/9 < 0: d/9 = - 6 & (II)

lcd/9=6 & (I) d/9=- 6 & (II)

(I), (II): LHS * 9=RHS* 9

ld_1=54 d_2=- 54

Both 54 and - 54 are solutions to the given equation. Let's graph these solutions on a number line.