Exercise 49 Page 211

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

d=-9 or d=9

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

|2d|+3=21

SubEqn

LHS-3=RHS-3

|2d|+3-3=21-3

SubTerms

Subtract terms

|2d|=18

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

|2d|= 18 This equation means that the distance is 18, either in the positive direction or the negative direction. |2d|= 18 ⇒ l2d= 18 2d= -18 To find the solutions to the absolute value equation, we need to solve both of these cases for d.

| 2d|=18

lc 2d ≥ 0:2d = 18 & (I) 2d < 0:2d = - 18 & (II)

lc2d=18 & (I) 2d=-18 & (II)

(I), (II): .LHS /2.=.RHS /2.

ld_1=9 d_2=-9

Both 9 and -9 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 49 Page 211

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