Exercise 30 Page 211

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

n=-2 or n=2

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Before we can solve this equation, we need to isolate the absolute value expression using the Properties of Equality.

|-3n|-2=4

AddEqn

LHS+2=RHS+2

|-3n|-2+2=4+2

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Add terms

|-3n|=6

An absolute value measures an expression's distance from a midpoint on a number line.

|-3n|= 6 This equation means that the distance is 6, either in the positive direction or the negative direction. |-3n|= 6 ⇒ l-3n= 6 -3n= -6 To find the solutions to the absolute value equation, we need to solve both of these cases for n.

| -3n|=6

lc -3n ≥ 0:-3n = 6 & (I) -3n < 0:-3n = - 6 & (II)

lc-3n=6 & (I) -3n=-6 & (II)

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

ln_1=-2 n_2=2

Both n=-2 and n=2 are solutions to the absolute value equation.

Subchapter links

Lesson Check p.210

Practice and Problem-Solving Exercises p.211-213

Standardized Test Prep p.213

Mixed Review p.213

Exercise 30 Page 211

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