Exercise 55 Page 211

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

c=-0.2 or c=8.2

Practice makes perfect

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

-2|c-4|=-8.4

DivEqn

.LHS /(-2).=.RHS /(-2).

-2|c-4|/-2=-8.4/-2

CalcQuot

Calculate quotient

|c-4|=4.2

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

|c-4|= 4.2 This equation means that the distance is 4.2, either in the positive direction or the negative direction. |c-4|= 4.2 ⇒ lc-4= 4.2 c-4= -4.2 To find the solutions to the absolute value equation, we need to solve both of these cases for c.

| c-4|=4.2

lc c-4 ≥ 0:c-4 = 4.2 & (I) c-4 < 0:c-4 = - 4.2 & (II)

lcc-4=4.2 & (I) c-4=-4.2 & (II)

(I), (II): LHS+4=RHS+4

lc_1=8.2 c_2=-0.2

Both c=8.2 or c=-0.2 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 55 Page 211

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