Exercise 53 Page 259

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

-4,4

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

-2|5y|=-40

DivEqn

.LHS /-2.=.RHS /-2.

|5y|=20

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

|5y|= 20 This equation means that the distance is 20, either in the positive direction or the negative direction. |5y|= 20 ⇒ l5y= 20 5y= - 20 To find the solutions to the absolute value equation, we need to solve both of these cases for y.

| 5y|=20

lc 5y ≥ 0:5y = 20 & (I) 5y < 0:5y = - 20 & (II)

lc5y= 20 & (I) 5y=- 20 & (II)

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

ly_1= 4 y_2=- 4

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

Subchapter links

Lesson Check p.257

Practice and Problem-Solving Exercises p.257-259

Standardized Test Prep p.259

Mixed Review p.259

Exercise 53 Page 259

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