# Answer to Question #20258 in Trigonometry for Kristen Woods

Question #20258

solve each absolue value equation

8. |3/(k-1)|=4

8. |3/(k-1)|=4

Expert's answer

& |3/(k-1)|=4

|3/(k-1)| = 4& ==>

( 3/(k-1) = -4 ) and ( 3/(k-1) = 4 )& ==>

( -4(k-1) = 3 ) and ( 4(k-1) = 3 ) and k≠1& ==>

( -(k-1) = 3/4 ) and ( (k-1) = 3/4 ) and k≠1& ==>

( -k+1 = 3/4 ) and ( k-1 = 3/4 ) and k≠1& ==>

( -k = -1/4 ) and ( k = 7/4 ) and k≠1 ==>

( k = 1/4 ) and ( k = 7/4 ) and k≠1.

So, there are two different solutions of the given equation:

k = {1/4, 7/4}.

|3/(k-1)| = 4& ==>

( 3/(k-1) = -4 ) and ( 3/(k-1) = 4 )& ==>

( -4(k-1) = 3 ) and ( 4(k-1) = 3 ) and k≠1& ==>

( -(k-1) = 3/4 ) and ( (k-1) = 3/4 ) and k≠1& ==>

( -k+1 = 3/4 ) and ( k-1 = 3/4 ) and k≠1& ==>

( -k = -1/4 ) and ( k = 7/4 ) and k≠1 ==>

( k = 1/4 ) and ( k = 7/4 ) and k≠1.

So, there are two different solutions of the given equation:

k = {1/4, 7/4}.

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