Trick question?...Solve 6|y-5|-8>10

Question

Answers correct?

y>8, y<2

y>-8, y<-2

 

Are all real numbers solutions?... no

Is there a solution?...  yes

Answer 1

Hi, Stephen.

 

For this problem, first let's isolate the absolute value.

6|y-5| - 8 > 10

6|y-5| - 8 + 8 > 10 + 8

6|y-5| > 18

[6|y-5|]/6 > 18/6

|y-5| > 3

 

So, our y values are those for which |y-5| is greater than 3 or, when..

y - 5 > 3 or y - 5 < - 3

 

y - 5 + 5 > 3 + 5

y > 8

 

y - 5 + 5 < -3 + 5

y < 2

 

So, y>8 or y<2 is the correct answer.

In interval notation (-inf,2)U(8,inf).

 

Please let me know if this is not solved clearly enough.