Exercise 5 Page 105

How many cases do you have after you remove the absolute value?

Solutions: {-2,4}
Number Line:

Practice makes perfect

An absolute value measures an expression's distance from a midpoint on a number line. |3z-3|= 9 This equation means that the distance is 9, either in the positive direction or the negative direction. |3z-3|= 9 ⇒ l3z-3= 9 3z-3= - 9 To find the solutions to the absolute value equation, we need to solve both of these cases for z.

| 3z-3|=9

lc 3z-3 ≥ 0:3z-3 = 9 & (I) 3z-3 < 0:3z-3 = - 9 & (II)

lc3z-3=9 & (I) 3z-3=-9 & (II)

(I), (II): LHS+3=RHS+3

lc3z=12 & (I) 3z=-6 & (II)

(I), (II): .LHS /3.=.RHS /3.

lz_1=4 z_2=- 2

Both -2 and 4 are solutions to the absolute value equation. Let's graph these solutions on a number line.

Subchapter links

Check Your Understanding p.105

Practice and Problem Solving p.106-108

H.O.T. Problems p.108

Standardized Test Practice p.109

Spiral Review p.109

Skills Review p.109

Exercise 5 Page 105

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