Exercise 58 Page 117

An absolute value measures an expression's distance from a midpoint on a number line. |5c-8|= 12This equation means that the distance is 12, either in the positive direction or the negative direction. |5c-8|= 12 ⇒ l5c-8= 12 5c-8= - 12 To find the solutions to the absolute value equation, we need to solve both of these cases for c.

| 5c-8|=12

lc 5c-8 ≥ 0:5c-8 = 12 & (I) 5c-8 < 0:5c-8 = - 12 & (II)

lc5c-8=12 & (I) 5c-8=- 12 & (II)

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

l5c=20 5c=-4

(I), (II): .LHS /5.=.RHS /5.

lc=4 c= -45

MoveNegNumToFrac

(II):Put minus sign in front of fraction

lc_1=4 c_2=- 45

Both 4 and - 45 are solutions to the absolute value equation.