Exercise 51 Page 259

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

- 31, 9

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An absolute value measures an expression's distance from a midpoint on a number line. 20=|n+11|⇔ |n+11|= 20This equation means that the distance is 20, either in the positive direction or the negative direction. |n+11|= 20 ⇒ l|n+11|= 20 |n+11|= -20 To find the solutions to the absolute value equation, we need to solve both of these cases for n.

20=|n+11|

lc n+11 ≥ 0:n+11 = 20 & (I) n+11 < 0:n+11 = - 20 & (II)

lcn+11=20 & (I) n+11=-20 & (II)

lc$LHS-11=RHS-11$ & (I) $LHS+11=RHS+11$ & (II)

ln_1=9 n_2=-31

Both 9 and -31 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 51 Page 259

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